Interference cancellation

ABSTRACT

A method implemented in an access point (AP) having N antennas used in a wireless communications system including two first client devices each of which has M antennas and two second client devices each of which has N antennas, where M and N are even is disclosed. The method comprises: performing interference alignment (IA) in common vector spaces; and delivering M+N streams. Other methods, systems, and apparatuses also are disclosed.

RELATED APPLICATION INFORMATION

This application is a division of co-pending patent application Ser. No.14/560,723, entitled ‘DEGREES OF FREEDOM IN MULTICELL WIRELESS SYSTEMSWITH FULL-DUPLEX BASE STATIONS USING INTERFERENCE ALIGNMENT AND METHODSFOR ENABLING FULL-DUPLEX WITH HALF DUPLEX CLIENTS’ and filed on Dec. 4,2014, which is incorporated herein by reference and in turn claimspriority to provisional application Ser. No. 61/949,613 filed on Mar. 7,2014, which is incorporated herein by reference, and provisionalapplication Ser. No. 61/911,627 filed on Dec. 4, 2013, which is alsoincorporated herein by reference.

BACKGROUND

1. Technical Field

The present invention relates to strategies for enabling full duplexwireless systems. More particularly, the present disclosure is relatedto using interference alignment for enabling duplex wireless systemsand/or enabling full duplex wireless systems using half duplex clients.

2. Description of the Related Art

In order to increase the spectral efficiency in wireless communicationsystems, several improvements have been performed in the past decades.Besides having better coding and modulation schemes, using feedback, andmultiuser interference cancellation, the most notable strategy has beenthe use of multiple antenna systems. Multiple input multiple output(MIMO) systems can generate a more reliable channel through diversity intransmitting the signal in multiple channels between the transmit andreceive antennas, where each channel goes through a different path andpotentially has independent fading or moderate to low correlation toother signal paths. The use of MIMO has shown to increase the capacityas well, where multiple signal streams are transmitted in differentspatial dimension of the channel. Nonetheless, increasing the number ofantennas results in more complicated demodulation, and decoding schemethat is very hard to achieve the optimal performance in practicalsystems. Hence, the practical use of multi stream transmission islimited to maximum of two streams in current standards (for examplerelease 12 LTE and all prior releases). More transmit and receiveantennas can be used for precoding or beam forming, e.g., up to 4antennas in release 9 LTE and 8 antennas in release 11 LTE. Yet,increasing the number of antennas increases the hardware complexity andcost, and each antenna requires a separate transmit and receive RFchains.

REFERENCES

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SUMMARY

The present disclosure is directed to increasing spectral efficiency inwireless communication systems. In one embodiment, an interfacealignment system for communication structures is provided that includesa single cell channel comprising an access point node and a fullbipartite interference channel (FBIC) configuration of a plurality ofreceiving nodes and a plurality of transmitting nodes, wherein eachreceiving node sees an interfering signal from all transmitting nodes.The access point to the single cell channel provides a single nodehaving downlink channels to all receiving nodes in the FBICconfiguration, and all of the uplink channels from the FBIC channel areto the single node that provides the access point to the single cellchannel.

In another aspect of the present disclosure, a method of full-duplexcommunication in a wireless network is provided that may includesimultaneous transmission to a plurality of receiving users andsimultaneously receiving from a plurality of transmitting users in fullduplex, wherein the transmission of the transmitting users are alignedat the receiving users. In some embodiments, the plurality oftransmitting users and the plurality of receiving users are half duplex.Each user may be equipped with multiple antenna and alignment ofinterfering signal of the transmitting users at the receiving users canbe performed in spatial domain. Linear precoding or filtering may alsobe used at the transmitters or the receivers to mitigate theinterference. In some embodiments, the plurality of transmitting usersand receiving users may be composed of two transmitting users and tworeceiving users that are active. The alignment that is performed by atleast one of communication nodes may be in a distributed manner. Thecontrol signal may be communicated between the users directly.

In yet another aspect of the present disclosure, a computer programproduct is provided that includes a computer readable storage mediumhaving computer readable program code embodied therein for performing amethod of full-duplex communication in wireless network. The method mayinclude simultaneous transmission to a plurality of receiving users andsimultaneously receiving from a plurality of transmitting users in fullduplex, wherein the transmission of the transmitting users are alignedat the plurality of receiving users. In some embodiments, the pluralityof transmitting users and the plurality of receiving users may be halfduplex.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a schematic of a single cell channel, in accordance with oneembodiment of the present disclosure.

FIG. 2 is a schematic of a full bipartite interference channel (FBIC),in accordance with one embodiment of the present disclosure.

FIG. 3 is a schematic of a full bipartite interference channel (FBIC)including transmit and receive precoding filters and interpretation ofchannel reduction, in accordance with one embodiment of the presentdisclosure.

FIG. 4 is a schematic of one embodiment of the degrees of freedom in asymmetric full bipartite interference channel (FBIC), in accordance withthe present disclosure.

FIG. 5 is a schematic depicting the degrees of freedom available in oneembodiment of a symmetric 2,2 FBIC.

FIGS. 6-13 are schematics of other embodiments of full bipartiteinterference channel (FBIC) configurations for use with the method,systems and computer program products of the present disclosure.

FIG. 14 is a schematic of two cells including full bipartiteinterference channel (FBIC) interference configurations, in accordancewith one embodiment of the present disclosure.

FIG. 15 is a schematic of a multi-cell channel having FBIC between usersin each cell, and showing the interference from adjacent cells, inaccordance with one embodiment of the present disclosure.

FIG. 16A is a schematic of interference alignment to addressuplink-downlink interference (UDI) in a full duplex (FD) wirelessnetwork, in accordance with one embodiment of the present disclosure.

FIG. 16B is a schematic of interface alignment in a half duplex (HD)wireless network, in accordance with the present disclosure.

FIGS. 17A-17D are schematics comparing network interference between halfduplex (HD) and full duplex (FD) wireless networks, in accordance withthe present disclosure.

FIGS. 18A and 18B are schematics depicting symmetric full duplexinterference channel (FDIC) configurations, in accordance with someembodiments of the present disclosure.

FIGS. 19A-19C are schematics depicting interference alignment networks,in accordance with some embodiments of the present disclosure.

FIGS. 20A-20B are schematics depicting examples of interface alignmentconstruction.

FIG. 21 is a timeline of a full duplex without strings (FDoS) systemoperation, in accordance with one embodiment of the present disclosure.

FIG. 22 is a block diagram of a system for providing full-duplexcommunication in a wireless network, in accordance with the presentdisclosure.

FIG. 23 depicts uplink-downlink Interference in FD Networks.

FIG. 24 depicts spatial interference alignment.

FIG. 25 shows SINR at the downlink client is affected by UDI from ULtransmission.

FIG. 26 depicts an interference network: HD vs. FD.

FIG. 27 depicts symmetric FDIC

FIG. 28 depicts an interference alignment network.

FIG. 29 depicts examples of IA construction.

FIG. 30 depicts an FDoS Operation Timeline.

FIG. 31 depicts an SINR increase at the DL nodes due to interferencealignment.

FIG. 32 depicts CDF of the SINR improvements due to FDoS.

FIG. 33 depicts the performance of FDoS as a function of the conditionnumber of the channel matrices.

FIG. 34 Shows FDoS achieves the same rate as a clean MUMIMOtransmission, even under strong UL interference.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Embodiment 1

One of the main challenges in deployment of full duplex systems in anetwork is the scaling of the promised doubling of the spectralefficiency by the full duplex operation when multi-user communicationand multiple antenna systems are considered. In one aspect, the methods,systems and computer program products disclosed herein address apractical way of solving this challenge in a wireless system consistingof a single cell or multiple cells with a full duplex access points.Interface alignment is proposed where all the uplink nodes attempt toalign their interferences only on a subset of resolvable degrees offreedom of each downlink user.

Further, enabling wireless full-duplex (from an access point (AP)) withmultiple half duplex (HD) clients is key to widespread adoption tofull-duplex (FD) commercial networks. However, enabling FD in suchnetworks is fundamentally challenged by a new form of uplink-downlinkinterference (UDI) that arises between HD clients operatingsimultaneously in the uplink and downlink directions of the full-duplexnetwork. In this context, it is shown that spatial interferencealignment (IA) between clients is an effective and scalable technique toaddress the uplink-downlink interference (UDI), and hence enable fullduplex (FD) in these networks, especially in the presence of multipleinput multiple output (MIMO) scenarios. In some embodiments, themethods, systems and computer program products that are disclosed hereinprovide full-duplex without strings (FDoS). In some embodiments, themethods, systems and computer program products build the theory ofapplying spatial interference alignment (IA) to full duplex methods ingeneral and present elegant, implementation friendly constructions forgenerating feasible interface alignment (IA) solutions that leverage thestructure of interference specific to these networks. In the process,the full-duplex without strings (FDoS) system shows that four halfduplex (HD) clients are both necessary and sufficient to eliminate UDIthrough IA and enable 2N streams at an N transceiver access point (AP).FDoS systems also enable an efficient media access control (MAC) designat the AP to handle clients with heterogeneous antenna capabilities,maximize the throughput of the enabled streams in the full duplex (FD)session, as well as reduce the overhead incurred in FDoS by half byfacilitating a distributed implementation. One key feature of thedisclosed methods and system is to realize full duplex communicationbetween multiple users that are in the same interference domain. Thisfeature allows the gain of full duplex technology to scale with theincreasing number of users.

It should be understood that embodiments described herein may beentirely hardware or may include both hardware and software elements,which includes but is not limited to firmware, resident software,microcode, etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable storage medium such as a semiconductor or solid statememory, magnetic tape, a removable computer diskette, a random accessmemory (RAM), a read-only memory (ROM), a rigid magnetic disk and anoptical disk, etc.

A data processing system suitable for storing and/or executing programcode may include at least one processor, e.g., a hardware processor,coupled directly or indirectly to memory elements through a system bus.The memory elements can include local memory employed during actualexecution of the program code, bulk storage, and cache memories whichprovide temporary storage of at least some program code to reduce thenumber of times code is retrieved from bulk storage during execution.Input/output or I/O devices (including but not limited to keyboards,displays, pointing devices, etc.) may be coupled to the system eitherdirectly or through intervening I/O controllers.

The use of full duplex systems can potentially revolutionize the hardthreshold on spectral efficiency where in theory the spectral efficiencyof a single link can be doubled in comparison to half duplex (HD)systems. A “duplex communication system” is a point-to-point systemcomposed of two connected parties or devices that can communicate withone another in both directions. There are two types of duplexcommunication systems: full-duplex and half-duplex. In a full duplexsystem, both parties can communicate to the other simultaneously. In ahalf-duplex system, in contrast, each party can communicate to theother, but not simultaneously; the communication is one direction at atime. Recent work on FD wireless systems has considered the use ofmultiple antennas for cancellation of the self interference (SI),however the number of RF chains would not increase for the additionalantennas used for the purpose of SI cancellation. The comparison of amultiple antenna system working in HD or FD shows the benefit of eithertechnology in different scenarios considering their algorithmic andhardware complexity. One issue is finding ways to enable FD withoutsacrificing MIMO performance. Another important problem is enablingmulti user communications in FD systems that seem to be a bottleneck inachieving the promised 2 times spectral efficiency for single link FDsystem. The main issue is that when multiple users are communicatingwith a single node (base-station or access point), their uplink signalcauses interference to the downlink signal transmitted from the accesspoint which are now both in the same frequency band. Therefore, the mainproblem is to address the uplink interference in the downlinktransmissions. This issue has been noticed and formalized be severalprior works. A prior art in addressing the uplink interference indownlink transmission uses a different frequency band that is not usedby the base station to share the uplink interference signal between theusers. This solution relies on availability of a different frequencyband and the assumption that this band cannot or may not be used by theaccess point.

In some embodiments, the methods, systems and computer program productsdisclosed herein address the self interference by interference alignmentand cancellation. In some embodiments, the methods, systems and computerprogram products disclosed herein propose a scheme that requires lesssignaling between the users and access point, which can be done in thesame frequency band that is used by the access point. In someembodiments, the channel state information between the users is used bythe methods disclosed herein in a central entity, e.g., the accesspoint, to compute a set of precoders to be used by the users and accesspoint with the goal of eliminating or reducing interference of theuplink users on the downlink transmission. In some embodiments, eachinvolved uplink user sacrifices part of its degrees of freedom (thenumber of independent streams that could be transmitted in the uplink)in order to align its interference with other involved uplink users onthe downlink users leaving the downlink users with some degrees offreedom (the number of independent streams that can be received by adownlink user).

In some embodiments, constructing a full duplex node can be moreefficient and can be easier for the access points and it is desirable tohave half duplex clients for the sake of simplicity, power consumption,as well as better handling of the mobility. In one example, the methods,systems and computer program products disclosed herein present a schemein which four users are picked from the pool of users. For the sake ofsimplicity, it is assumed that each user and the access point have Nantennas. The case of users and access points with different number ofantennas can be handled similarly. For example, it can be scheduled thattwo users are in the uplink and two users are in the downlink. By usinginterference alignment two uplink users only use N/2 out of their Ndegrees of freedom to transmit data in the uplink to the access point,while by using a linear precoding, they align the interference that theycause to the two downlink users in only N/2 dimensions such that eachdownlink user is left with N/2 degrees of freedom to receive streamsfrom the access points, as depicted in FIG. 5. FIG. 5 depicts thedegrees of freedom available in one embodiment of a symmetric 2,2 FBIC.As a result the total of 2N degrees of freedom can be used to transmit2N streams, where N degrees of freedom are used in the uplink and Ndegrees of freedom are used in the downlink. It is noted that in priorart systems using MU-MIMO (multi-user MIMO), only N degrees of freedomcan be achieved in either downlink or uplink. Even if interferencecancellation or interference alignment is used in conjunction withMU-MIMO, the maximum degrees of freedom would remain as N. Hence, theuse of full-duplex access point can in fact double the spectralefficiency in a single cell by using intelligent interference alignmenttechnique.

The methods, systems and computer program products employ arevolutionary fact that doubling the number of possible transmit andreceive streams is possible. More particularly, in the high signal tonoise ratio (SNR) regime, the scaling of a total transmit and receiveinformation by a full duplex access point in a single cell is twice asmuch as that of a half-duplex access point in a single cell. Themethods, structures and systems disclosed herein characterize theachievable and maximum possible scaling factor in multi-cell systems.

Although the focus of the methods, systems and computer program producesmay be on the degrees of freedom achievable through transmit and receiveprecoder (filter) design, the actual design of the precoders may beconsidered in terms of other system measures, such as the receivedsignal power RSSI, signal to noise ratio, or a capacity measure. Forsimplicity of the discussion and without loss of generality, theprecoders may be considered to be semi-orthogonal matrices, which meansthey are formed by selecting rows or columns of a unitary matrix.However, in other embodiments, given a total dimension of a precoder,the precoder does not have to be a semi-unitary matrix. In other words,the rows or columns of the precoding matrices might not be orthogonal.The latter condition would allow for the design of more efficientfilters that can achieve, e.g., better capacity or throughput in low ormid range of signal to noise ratio. Nonetheless, all such precoderswould follow the same degree of freedom at high SNR and have the samescalability factor. In some embodiments, it is possible to perform theinterference alignment in distributed form, in which each node performsthe calculation of the precoders individually or based on some feedbackfrom other nodes.

In some embodiments, the methods, systems and computer program productsemploys a channel model that considers a communication channelconsisting of L transmitting nodes which have intended signal for asingle node called access point or base station and K receiving nodesthat receive signal from the same access point. A memory less channel isconsidered to be present between all pair of the nodes that can beaccessed simultaneously and the transmission is received by a singlenode from all transmitting point that are active simultaneously. Thismeans that part of the channel may be used by considering some of thetransmit signals to be zero, for example, when the access point works inhalf duplex mode it can either transmit to all or a subset of receivingnodes and the access point will not receive any signal from thetransmitting point. However, in the same scenario, if the transmittingnode beside the access point start a simultaneous transmission with theaccess point it would cause an interference with the potential receivingpoints. A half duplex access point can also receive from all or a subsetof transmitting points when it has stopped transmission to the receivingnodes. The transmitting node may also be called the uplink nodes oruplink users and the channel between these nodes and the access point isalso called uplink channel. Similarly, the receiving node may also becalled downlink nodes or downlink users and the channel between them andthe access point is called downlink channel.

A full duplex access point can transmit in the downlink while itreceives in the uplink. However, the situation where a full duplexaccess point is used is very different from the case where a half duplexaccess point is deployed. In the latter case, the uplink channel is usedseparately from the downlink channel, hence, there is no interference inon the downlink users from the uplink transmission. However, in theformer case, where a full duplex access point is used, the possibilityof using the full potential of the downlink and uplink channelsimultaneously is limited by the fact that the downlink users aresuffered from the interference caused by the uplink transmissions.

The following description provides some embodiments of how the methods,systems and computer program products disclosed herein address aninterference management technique in a single or multiple cells wherethe communication channel in each cell is defined by the channel modelpresented in this section.

As it is illustrated in the schematic of the single cell channel (SCC)that is depicted in FIG. 1, the channel H₁₁, H₁₂, H₂₁, H₂₂, H₁₁, H₂₁,H_(k1), H_(k2), is composed of a full bipartite graph between the uplinknodes and downlink nodes, as well as a multiple access channel H_(0I),H₀₂, H₀₁ from all the uplink nodes x₁, x₁, x₂, to the access point y, x,and a broadcast channel H_(0I), H₀₂, H₀₁ from the access point y,x toall downlink nodes y₁, y₁, y₂. Since the interference management is thecrucial part of enabling full duplex communication in a single cell, weconcentrate on the possible degrees of freedom that are achievable inthe full bipartite interference channel (FBIC) between uplink anddownlink nodes, which is illustrated in FIG. 2. Considering only theFBIC (FIG. 2), the received signal at each downlink node j, j=1, 2, . .. , K is given by:

y _(j)=Σ_(i=1) ^(L) H _(jiXi+Zj)  Equation (1)

where y_(j) is a vector of size N_(r,j), X_(i) is the vector of transmitsignal of size N_(t,i), and H_(ji) represent the channel between thetransmitter I and the receiver j that is a matrix of sizeN_(r,j)×N_(t,i) with entries that are independent and identicallydistributed (i.i.d.) circularly symmetric complex numbers with mean zeroand variance σ². The total received signal in the original single cellchannel (SCC) illustrated in FIG. 1 with transmission from the accesspoint is given by:

y _(j) +H _(j) ₀ _(X) ₀   Equation (2)

where x₀ is the transmitted vector from the access point and H_(j0) isthe channel from the access point to the receiver j. The received signalat the access point is given by:

y ₀=Σ_(i=1) ^(L) H _(0i) X _(0i)  Equation (3)

where y₀ is a vector of size N_(r,0) and H_(0i) represent the channelbetween the transmitter i and the access point. The noise at eachreceiver is represented by z_(j) (subscript zero means the access point)that is a vector of zero mean unit variance circularly symmetric complexwhite Gaussian noise.

Interference Alignment in FBIC

In order to maximize the uplink and downlink throughput, theinterference received at the downlink users from the uplink nodes haveto be mitigated. Different approaches for interference alignment existthat could include symbol level interference alignment, e.g., by usinglattice codes, or by using linear precoding to mitigate interference intime domain, subcarrier domain, space domain (for multiple antennasystems) or a combination of the three. The interference management intime domain might need the use of channel extension, and assumption ofhaving time varying channel. There are several practical considerationwith channel extension in time domain. For example, the channel has tobe time varying with a rate that we get enough random channelrealization in order to perform linear precoding and possibleinterference alignment that is effective, while the assumption ofknowing the channel at the transmitter forces a slow variation in thechannel so that the channel can be estimated and more importantly tohave small channel estimation overhead in comparison to the time thatthe channel estimates are valid to be used for the actual datatransmission.

The interference alignment in the subcarrier domain may be donesimilarly as the one in the space domain. Therefore, it is possible toconsider subcarriers as different antennas and convert the system to amultiple antenna system with a larger number of antennas. It is notedthat this transformation might change the channel properties, e.g., itmight introduce a correlation between the channel coefficients.

For practical reason, we focus on the interference alignment in spacedomain where the channel coefficients are fixed. We consider a fixedprecoder per block or multiple block of transmission within the channelcoherence time where the channel coefficients are approximatelyconstant. As shown in FIG. 3, a transmit precoding matrix V_(i), i=1, 2,. . . , L is considered at each transmission node and a receiver filteror a receive precoding matrix U_(j),j=1, 2, . . . , K at each receivingnode. FIG. 3 depicts full bipartite interference channel (FBIC)depicting transmit and receive precoding filters and interpretation ofchannel reduction. The transmit precoding matrices V_(i) are ofdimensions N_(t,i)×d_(t,i) where d_(t,i)≦N_(t,i) and receive filtersU_(j) are of dimension d_(r,j)×N_(r,j). It is noted that the precodingmatrices V_(i) and U_(j) are both required to be full rank, and forsimplicity are considered to be semi-orthogonal matrices, which meansthat the rows of U_(j) (the columns of V_(i)) are orthonormal (mutuallyorthogonal and have unit norm). The alignment condition is then givenby:

U _(i) H _(ij) V _(j)=0 ∀i=1,2, . . . ,L, and j=1,2, . . . ,K  Equation(4)

It is noted that the alignment conditions may be written in terms ofrows of U_(i)=[u_(i) ¹ u_(i) ² . . . u_(i) ^(d) ^(r,i) ] and columns ofV_(j)=[v_(j) ¹v_(j) ² . . . v_(j) ^(d) ^(r,j) ]. Under thesecircumstances, all vectors u_(i) ^(a) and v_(j) ^(b) for a given i and jand for all indices a and b satisfy the same equation:

u _(i) ^(a) H _(ij) v _(j) ^(b)=0  Equation (5)

In some embodiments, the above condition provides two conditions thatcan be necessary. First, the degrees of freedom of a receiving node jthat is the number of independent vectors cannot be more than thedimension of the vector space that contains this vector, henced_(t,j)≦N_(t,j). Similarly, for u_(i) ^(a) we have d_(r,i)≦Nr, I thatcan be the second necessary condition. There are two more conditionsthat can be deduced from Equation (5). In some embodiments, a thirdnecessary condition may be given by d_(r,i)+d_(t,j)≦max N_(r,i),N_(t,j). This is true due to the fact that if N_(r,i)≧N_(t,j) for agiven i and j all vectors H_(ij)v_(j) ^(b) have to be linearlyindependent since H_(ij) is generic and furthermore they are orthogonalto all u_(i) ^(a), which means that the total number of such vectors areless than the dimension of the vector u_(i) ^(a) that is N_(r,i).

In some embodiments, the fourth necessary condition may be obtained bycounting the number of scalar variables and scalar equations orconstraint that the variable have to satisfy. The intuition obtainedfrom the linear algebra is that a system of linear equation most likelydoes not have a solution if the number of variables are less than thenumber of constraint is the coefficients of the equations are generic.In some embodiments, it is possible to consider a set of constraintsthat are not linearly independent, e.g., if the coefficients are notgeneric, which means that the system might have a solution when thereare artificially more constraints than the variables but in fact thenumber of algebraically independent constraints are in fact lower thanthe number of variables.

The number of variables in a subset of equations S between the transmitand receiving node pair (i, j) is given by

+

d_(r,i)) where:

S⊂M={(i,j),1≦i≦L,1≦j≦K}  Equation (6)

The number of scalar equation in the same set is given by

. Therefore, the fourth necessary condition can be provided by:

+

≧

  Equation (7)

In the case that multiple cells are deployed, the coordination betweenthe access point can be key. For example, considering a traditional halfduplex system with multiple cells. The interference caused by the usersor access point in one cell will affect the users and the access pointin the other cell, hence the achievable throughput in adjacent cell candrop. However, the coordination between the access point can potentiallymake the system to work as a multiple antenna system, where the antennasare distributed in different locations. The level of coordinationbetween the access point, however, is a function of available backhaul(its capacity and its latency) between the access points. TheCoordinated Multi-Point (CoMP) transmission and reception has been oneof the study items in recent standards. The downlink CoMP is usuallyeasier to implement due to the fact that all precoding calculations andencoding process may be performed at a central location, and thenforwarded to the access points that are involved in transmission. On theother hand, realization of uplink CoMP with processing in a centrallocation may require transmission of the received signals in thebackhaul. Since the computed signals in downlink CoMP are in digitalform it is usually much easier to be sent in the backhaul while thedimension of the uplink received signals even after analog-to-digitalconversion are much larger than the signals that need to be transmittedto enable downlink CoMP. Therefore, it might be desirable to alsoconsider systems that deploy downlink CoMP, but not the uplink CoMP. Insome embodiments of the systems, methods and computer program productsdisclosed herein, it is assumed that full downlink and uplink CoMP isdeployed by base stations in either scenario of systems with half duplexaccess points or full duplex access points.

The full bipartite interference channel (FBIC) that has been describedabove with reference to FIGS. 1, 2, 3 and 5 is distinguishable fromtypical interference channels. The channels may seem to havesimilarities at a first glance. Both channels are multi-user channel,there are a set of transmitters and another set of nodes that arereceivers. Each receiver sees multiple interfering signals. However,there the number of transmitting nodes and receiving nodes in aconventional, i.e., non-FBIC, interference channel are always equal, andthere is a one to one correspondence between each transmitting node to areceiving node. The intended signal that are received by each receiveris the signal that is transmitted from the corresponding transmittingpoint. Therefore, with for example K transmit-receive pairs, there areonly K degrees of freedom in the channel where degrees of freedom are infact associated with K direct links between the corresponding transmitand receive pairs.

However, the degrees of freedom for an FBIC channel may be defined pernode. This means that that the degrees of freedom for each transmittingnode can be equal, but the degrees of freedom for the receiving nodescan be different. For example, the degrees of freedom of each of thetransmitting node could be equal to 2, while degrees of freedom of allreceiving nodes can be equal to 1. This means that each transmittingnode can in fact transmit in two independent and orthogonal direction.While the transmitting node interferes with all receiving nodes, thetransmitting node of the FBIC channel provides at least with one degreeof freedom, or one channel direction, that is interference free, andhence can be used by another node, e.g., the access point to receiveinformation. This situation is very different from the one in the(non-FBIC) interference channel, where degrees of freedom are definedper direct link between the corresponding transmit-receive pair, and itis not useful to have a transmit precoder or a receive filter that ispotentially has larger dimension than the other one.

In the following paragraphs some examples of designs and bound forinterference alignment in FBIC type channels is provided. For example(referred to hereafter as Lemma 1), the maximum degrees of freedom in a(2,2) FPIC channel with N antenna, e.g., virtual antenna, at each node,e.g., transmission and receiving nodes, may be equal to 2N, as depictedin FIG. 4. FIG. 4 depicts one embodiment of the degrees of freedomavailable in a symmetric (2,2) FBIC. In this example, V₁ and V₂ can bethe transmit precoding filters (as depicted in FIG. 3) and U₁ and U₂ canbe the receive precoding filters (as depicted in FIG. 3). The followingequation is to be satisfied:

U _(i) H _(ij) V _(j)=0 ∀i=1,2, and j=1,2  Equation (8)

Letting d_(t,i) and d_(r,i), i=1, 2 denote the degrees of freedom oftransmitting notes and receiving nodes, respectively. Counting, thenumber of variables and equations, results in the following:

Σ_(i=1) ² d _(t,i)(N−d _(t,i))+d _(r,i)(N−Nd _(r,i))≧Σ_(i=1) ²Σ_(i=1) ²d _(t,i) d _(r,j)  Equation (9)

Rearranging the above inequality in Equation (9) provides the following:

(d _(t,1) +d _(t,2) +d _(r,1) +d _(r,2))N≧Σ _(i=1) ² d _(t,i) ²+Σ_(i=1)² d _(i=1) ²+Σ_(i=1) ²Σ_(i=1) ² d _(t,i) d _(r,j)  Equation (10)

≧Σ_(i=1) ² d _(t,i) ²+Σ_(i=1) ² d _(r,i) ²+Σ_(i=1) ²Σ_(i=1) ² d _(t,i) d_(r,j)−(d _(t,1) −d _(t,2))²−(d _(r,1) −d _(r,2))²  Equation (11)

≧½(d _(t,1) +d _(t,2) +d _(r,1) +d _(r,2))²  Equation (12)

Hence providing:

(d _(t,1) +d _(t,2) +d _(r,1) +d _(r,2))≦2N  Equation (13)

In another example (referred to as Lemma 2 and reduction lemma), if byusing a particular set of transmit and receive filters, a set of degreesof freedom is achievable, it can be possible to rewrite all the channelswith a different number of transmit and receive antennas that are equalto the achievable degrees of freedoms at each node where the channelgain between the pair of the nodes (where interference has been takencare of) is equal to zero. For example, making the assumption that thetransmit precoders V_(i), i=1, 2, . . . , L and the receive filters Uj,j=1, 2, . . . , K have been used at uplink and downlink nodes. Thesignal seen at the receiver j can be rewritten as y′_(j)=U_(j)y_(j) andthe transmit signal at the transmitting node i is given byx_(i)=v_(j)x′_(i). In view of the above, the following is provided:

y _(j)=Σ_(i=1) ^(L) H _(ji) x _(i) +z _(j)  Equation (14)

y′ _(j)=Σ_(i=1) ^(L) U _(j) H _(ji) V _(i) x′ _(i) +z′ _(j),  Equation(15)

where z′_(j)=U_(j)z_(j). Therefore, the equivalent channel can beconsidered as H′_(ji)=U_(j)H_(ji)V_(i) that is the matrix of sized_(r,j)×d_(ti). In some embodiments, the selection of transmit precodersand receive filters may only cancels out the interferences betweenparticular subgroups of the nodes where U_(j)H_(ji)V_(i) is zero onlyfor particular values of i and j for which the corresponding channelsare zero. In some embodiments, the reduction lemma allows for a fullinterference alignment solution for a complicated problem to be brokendown in multiple stages. For example, in some embodiments, by using thereduction lemma it is possible to find simple algebraic solution to theinterference alignment problem in large channels.

In another example (referred to as Lemma 3), a total degrees of freedombeing equal to 2N is achievable using any split of d,d≦N at bothtransmit points, and N−d at both receiving nodes in a (2,2) FBICchannel, as depicted in FIG. 4, with N antenna at each node. As in proofof Lemma 1, V₁ and V₂ can be the transmit precoding filters of size N×dand U₁ and U₂ can be the receive precoding filters of size N×(N−d). Thefollowing has to be satisfied:

U _(i) H _(ij) V _(j)=0 ∀i=1,2, and j=1,2  Equation (16)

V₁ and V₂ are selected such that span(H₁₁V₁)=span(H₁₂V₂) in order toalign the interferences of both transmitting nodes into the same spaceof size N×d dimensions at the receiving node 1. Such selection is easyas for any choice of the precoding matrix V₁, the precoding matrix V₂can be obtained by choosing V₂=H₁₂ ⁻¹H₁₁V₁ where for random matrices Hij this can be done with probability 1. In order to align theinterferences of both transmitter to the receiving node 2, we must havespan (H₂₁V_(i))=span(H₂₂V₂), hence we have span(V₁)=span(H₁₁ ⁻¹H₁₂V₂).In order to satisfy both alignment conditions, we have span(V₁)=span(H₁₁⁻¹H₁₂H₁₂ ⁻¹ H₁₁V₁). This means that V_(i) can be composed of any deigenvectors of the matrix H₁₁ ⁻¹H₁₂H₁₂ ⁻¹H₁₁ and V₂=H₁₂ ⁻¹H₁₁V₁. Underthese conditions the space of signals at both receiving nodes is limitedto a d dimensions and hence there exist N−d orthogonal dimensions ateach receiving nodes, which can be used to construct N×(N−d) dimensionalreceive filters U₁ and U₂.

In another example (referred to as Lemma 4), in a single cell with afull duplex access point with N transmit and N receive RF chains and(K−t,K) FBIC with L transmitting nodes with degrees of freedom d_(t,i),i=1, . . . , L, and K receiving nodes with degrees of freedom d_(r,i),i=1, . . . , K, the total simultaneous uplink and downlink streams isequal to:

min(N,Σ _(i=1) ^(L) d _(t,i))+min(N,(Σ_(i=1) ^(K) d _(r,i)))  Equation(17)

Proof for the validity of Equation (17) relies on the fact that thetransmitting nodes have total of Σ_(i=1) ^(L)d_(t,i) degrees of freedomto transmit in uplink to a full duplex access point without causinginterference on total of Σ_(i=1) ^(K), d_(r,i) degrees on freedomavailable to the receiving point that receive signals from the same fullduplex access point in the downlink. However, the number of transmittedstream in the downlink and received stream in the uplink by the accesspoint can also be limited by the number of RF chain (or correspondingantenna) in each direction. Assuming the number of antennas for thepurpose of transmission or reception or equivalently, the number of RFchain in the receive path and transmit path are both equal to N that isthe same as the number of antennas for each node in FBIC, the totalstream in the uplink and downlink is also bounded by N. The uplinkchannel between the transmitting node and the access point isindependent of the intranode channels in FBIC, hence, the transmittedsignal to the access point are received in generic direction, whichmeans that up to the N of them are independent. In some embodiments, thenumber of antenna at the access point could be different from the numberof antenna at the FBIC. For example, the number of access point antennamight be larger than the number of antennas at the transmitting point,and still due to the fact that the uplink channels are generic, thenumber of resolvable directions would be only limited by the number ofantennas at the access point rather than the dimension of transmittingvectors. The same arguments hold true for the downlink channel betweenthe access point and the receiving nodes.

FIG. 6 depicts the degrees of freedom that are achievable in a symmetric(4,4) FBIC with algebraic construction (N=4 antennas per node). FIG. 7depicts the degrees of freedom that are achievable in a symmetric (4,4)FBIC with N=3 antennas per node.

In yet another example (referred to as Lemma 5), a maximum of the totaldegrees of freedom in a (K,K) FBIC channel, as depicted in FIG. 8, witha symmetric d degrees of freedom and N antenna at each node is

$2K{\left\lfloor \frac{2N}{k + 2} \right\rfloor.}$

FIG. 8 depicts the degrees of freedom achievable (by algebraicconstruction) in a symmetric (K,K) FBIC with arbitrary number of nodes Kand number of antennas N per node. In this example, the number ofvariables have to be greater or equal to the number of constraint inorder to have a possible solution, in which:

$\begin{matrix}{{{\sum\limits_{i = 1}^{K}{d_{t,i}\left( {N - d_{t,i}} \right)}} + {d_{r,i}\left( {N - d_{r,1}} \right)}} \geq {\sum\limits_{i = 1}^{K}{\sum\limits_{i = 1}^{K}{d_{t,i}d_{r,j}}}}} & {{Equation}\mspace{14mu} (18)} \\{{2{{Kd}\left( {n - d} \right)}} \geq {K^{2}d^{2}}} & {{Equation}\mspace{14mu} (19)} \\{d \leq \frac{2N}{K + 2}} & {{Equation}\mspace{14mu} (20)}\end{matrix}$

In this example, there are 2K nodes each with degrees of freedom lessthan or equal to

$\frac{2N}{k + 2}$

that will add up to

$2K{\left\lfloor \frac{2N}{K + 2} \right\rfloor.}$

In a further example (referred to as Lemma 6), the maximum degrees offreedom in an arbitrarily large FBIC with maximum of N antenna at eachnode is not limited by N and can be made arbitrarily large. Consideringa (K,K) FBIC where the case that total uplink degrees of freedom islimited to N−1, i.e.:

Σ_(i=1) ^(K) d _(t,1) ≦N−1  Equation (21)

In this example, each node in the downlink has at least one degrees offreedom left. Hence, the total number of degrees of freedom in thesystem can be made at least as large as N−1+K. Therefore, in someembodiments, by increasing the number of downlink users, e.g.,increasing K, the total degrees of freedom in the system can growunboundedly and independent of the number antennas N. In someembodiments of this example, the total number of uplink user does notneed to increase with increasing K, and at most N−1 uplink user sufficesto reach the desired result. Lemma 6 reveals that the (K,K) FBIC withconstant gain has degrees of freedom scaling that is much better thaninterference channel even with time extension (time varying channel withchannel state information (CSI) at the transmitters) that is bounded byK/2.

In a further example (referred to as Lemma 7), an FBIC is consideredwith N antenna per node, wherein if either of the uplink or downlinkdegrees of freedom scales with the number of antennas N as (1+α)N thenthe other one cannot scale with a scaling factor more than (1+1/α). Insome examples, this can mean that both the uplink and downlink degreesof freedom cannot be made equal to 2N or larger simultaneously. Forexample, considering a (K,K) FBIC with N antenna at each node, in whichby counting the number of variables and constraints, the followingequations are provided:

Σ_(i=1) ^(K) d _(t,i)(N−d _(t,i))+d _(r,i)(N−d _(r,i))≧Σ_(i=1)^(K)Σ_(i=1) ^(K) d _(t,i) d _(r,j)  Equation (22)

N(Σ_(i=1) ^(K) d _(t,i)+Σ_(i=1) ^(K) d _(r,1))≧Σ_(i=1) ^(K) d _(t,i)²+Σ_(i=1) ^(K) d _(r,i) ²+Σ_(i=1) ^(K) d _(t,i)Σ_(i=1) ^(K) d_(r,j)  Equation (23)

In one example, when (1+α)N=Σ_(i=1) ^(K)d_(t,i) and (1+β)N=Σ_(i=1)^(K)d_(r,i) for some non negative real numbers α and β, Lemma 9 cansupport the existence of at least N uplink and N downlinksimultaneously. α and β may exist. However, for the purpose of findingthe upper bound, a and may be considered as negative values between −1and 0 to provide:

N((1+α)N+(1+β)N)≧Σ_(i=1) ^(K) d _(t,i) ²+Σ_(i=1) ^(K) d _(r,i)²+(1+α)N(1+β)N  Equation (24)

N ²(2+α+β)≧Σ_(i=1) ^(K) d _(t,i) ²+Σ_(i=1) ^(K) d _(r,i) ² +N²(1+α+β+αβ)  Equation (25)

N ²≧Σ_(i=1) ^(K) d _(t,i) ²+Σ_(i=1) ^(K) d _(r,i) ² +N ²αβ  Equation(26)

Therefore, in view of the above, αβ<1 or equivalently β<1/α, must bemet. This can mean that scaling in the uplink and downlink are boundedby (1−α)N and (1+β)N where

$\beta < {\frac{1}{\alpha}.}$

Hence, the scaling of 2N in the uplink and downlink is possiblesimultaneously. Further, based on Theorem 1 for large enough K it ispossible to approach arbitrarily close to this scaling.

FIG. 15 depicts an example of a multi-cell channel having FBIC betweenthe users in each cell, and showing the interference from other(adjacent) cells. FIG. 15 illustrates the uplink and downlink channel ineach cell between the users and the access points. FIG. 15 shows thebackhaul connection between the access points. In an yet another example(referred to as Lemma 8), the total degrees of freedom is equal toN(M+1)−1 in a M cell full duplex system, as depicted in FIG. 15, inwhich a maximum of N antennas per node and access point is achievable.This corresponds to the gain of

$1 + \frac{N - 1}{M}$

for using full duplex versus half duplex access points. Furthermore, insome embodiments, no scaling better than 1/(M−1) with respect to thenumber of cells is achievable; which means that the presented scheme isoptimal in terms of scaling. Using the construction presented in Lemma 6it is possible to have a (K,K) FBIC with N antenna per node that hastotal of N−1 degrees of freedom in the uplink and K degrees of freedomin the downlink. In some examples, by choosing K=MN, and dividing thereceiving nodes into M equal group of size N node each, and assigningeach group to a different access point total of MN degrees of freedom inthe downlink is available (based on Lemma 4).

On the other hand, any split of the nodes in the uplink would result intotal of N−1 degrees of freedom in the uplink simultaneously with MNdegrees of freedom in the downlink. Hence, the total degrees of freedomis equal to N(M+1)−1. Splitting the streams in the downlink into Mdifferent cells requires implementation of cooperative multi-pointtransmission (also known as CoMP) in the downlink. Based on reciprocityfor any configuration, the role of the transmit and receiving nodes inFBIC can be reversed without affecting the achievable degrees offreedom. Therefore, it is also possible to achieve total of MN degreesof freedom in the uplink and N−1 degrees of freedom in the downlink. Inthis scenario, the requirement of downlink-CoMP will be replaced withcooperative multi point reception or uplink-CoMP.

Comparing the full duplex access point with a half duplex access point,we can achieve a total of MN+N−1 degrees of freedom with full duplexaccess point versus the maximum of MN degrees of freedom with halfduplex access point. Hence the gain of using full duplex versus halfduplex access point

${G\frac{FD}{HD}\mspace{20mu} {is}\mspace{14mu} 1} + \frac{N - 1}{NM}$

which means that by increasing the number of access points

$G\frac{FD}{HD}$

only scales with

$\frac{1}{M}.$

Proceeding to characterizing the bound on the achievable scaling of

$G\frac{FD}{HD}$

by increasing the number of access point M, by using Lemma 7, theachievable scaling of the total degrees of freedom in the uplink anddownlink are bounded by (1+α)N and (1+β) N where β<1/α. In order to usethe full degrees of freedom in, for example, uplink, we can set(1+α)N=MN, and hence the total degrees of freedom in the downlink islimited to

$\left( {1 + \frac{1}{m - 1}} \right){N.}$

Using proper splitting of the transmit and receiving nodes of FBIC intoM cells it can be possible to achieve a total of MN+N+N/(M−1) streams.Therefore, the following equation is provided:

$\begin{matrix}{G_{\frac{FD}{HD}} = {\frac{{MN} + N + \frac{N}{M - 1}}{MN} = {1 + \frac{1}{M - 1}}}} & {{Equation}\mspace{14mu} (27)}\end{matrix}$

The upper bound on the scaling of

$G_{\frac{FD}{HD}}$

as a function of M is 1/M.

In another example (referred to as Lemma 9), for any (K,K) FBIC channelwith N=K antennas per node (e.g, as in FIG. 8), there may exist analgebraic construction of the transmit and receive vector that achievesdegree of freedom 1 per node, e.g., see FIG. 7 in which K=4. Forexample, the case of (2,2) has been handled in Lemma 3. In this example,the case of K=2k is considered, for k=2, 3, . . . etc. Referring to FIG.8, the transmit nodes are labeled by T1, T2, . . . , TK and receivingnodes are labeled by R1, R2, . . . , RK.

In this example, the transmit and receiving nodes are divided intogroups of two where the g^(th) group, g=1, 2, . . . , k, consists of thetransmitting nodes T_(2g-1) and T_(2g) and the receiving nodes R_(2g-1)and R_(2g). The methodology described above in Lemma 3 may be used totransmit in a single dimension from each transmitter and align thereceived interferences into a single dimension for each pair, leavingthe receiving nodes with K−1 degrees of freedom. The total number oftransmitters besides the transmitters in a given group is equal to K−2,hence, their received interference at this group cannot span more thanK−2 dimensions. Therefore, each receiver will have K−1(K−2)=1 degrees offreedom. Letting K=2k−1, for k=2,3, . . . the transmit and receivingnodes can be divided into groups of two except for the last group wherethe g^(th) group, g=1, 2, . . . , k−1, consists of the transmittingnodes T_(2g-1) and T_(2g) and the receiving nodes R_(2g-1) and R_(2g)and the last group consists of a single transmitting node T_(2k-1) and asingle receiving node R_(2k-1).

The methodology of Lemma 3 can be used to transmit in a single dimensionfrom each transmitter and align the received interferences into a singledimension for each pair g=1, 2, . . . , k−1, leaving the receiving nodeswith K−1 degrees of freedom. The receiving node R_(2k-1) will seeinterference from the first K−1 transmitters in an at most K−1dimensional space. Hence, this receiver is left with at least onedegrees of freedom and chooses its receive filter, accordingly. In someexamples, it can be important to make sure that the transmitter T_(2k-1)does not interfere with the receiver R_(2k-1) in this direction, hence,the transmitter T_(2k-1) can choose its transmit directions in only K−1dimension beside the dimension that after passing through the channelwill cause interference with R_(2k-1) in its only dimension.

The total number of transmitters besides the transmitters in a givengroup g=1, 2, . . . , k−1 and the last transmitter T_(2k-1) is equal toK−3, hence, their received interference at this group g=1, 2, . . . ,k−1 cannot span more than K−3 dimensions. Hence, each receiver g=1, 2, .. . , k−1 is left with K−1−(K−3)=2 degrees of freedom. The onlyinterferences that have not been accounted for are from the lasttransmitter T_(2k-1) to all the receivers of the group g=1, 2, . . . ,k−1. Using reciprocity, it is easier to exchange the role of thereceivers R_(g), g=1, 2, . . . , 2k and the transmitter T_(2k-1) andtheir effective channels that is obtained after performing the reductionof Lemma 2. It can be easily deducted that each pair R_(2g) andR_(2g)−1, g=1, 2, . . . , k can align their interferences at T_(2k-1) inthe same direction. Hence total of k degrees of freedom will be deductedfrom the last node T_(2k-1) leaving this node with K−k−1=k≧1 degrees offreedom. A simpler argument may also be made. Let all receiving nodesR_(g), g=3, 4, . . . , K only select one degree of freedom. Then, thenode TK will have K−(K−2)=2 degrees of freedom and the onlyinterferences that have not been accounted for are from the pair R1 andR2 to TK where each node has two degrees of freedom. Using the reductionin Lemma 2 it is easily observed that the interferences in thereciprocal channel from the pair R1 and R2 to the node TK can be alignedand this process will take away only one degree of freedom from eachinvolved node leaving these three nodes with one degree of freedom.

The following paragraph provides the details of theorem 1 that has beenreferenced in the above examples, i.e., Lemmas. In the followingtheorem, let N_(t,i), i=1: L and N_(r,i),i=1. K denotes the number ofantennas at the L transmitting nodes and K receiving nodes,respectively. The total degrees of freedom Σ_(i=1) ^(L)d_(t,i) in theuplink and Σ_(i=1) ^(K)dr, i in the downlink is achievable where d_(t,i)and d_(r,i) denote the degrees of freedom of the i^(th) node in theuplink and downlink, respectively, if and only if the followingconditions are satisfied:

+

≧

  Equation (28)

⊂

={(i,j),1≦i≦L,1≦j≦K}  Equation (29)

d _(t,i) ≦N _(t,i), and d _(r,i) ≦N _(r,i)  Equation (30)

d _(t,i) +d _(r,j)≦max N _(t,i) N _(r,j)  Equation (31)

FIG. 9 depicts the degrees of freedom achievable in a symmetric (3,3)FBIC with algebraic construction with N=3 antennas per node. FIG. 10depicts the degrees of freedom achievable in an asymmetric (4,3) FBIC(or equivalently in (3,4) FBIC) with algebraic construction (N=3antennas per node). FIG. 11 depicts the degrees of freedom available ina symmetric (3,3) FBIC with N=5 antennas per node. FIG. 12 depicts oneembodiment of an FBIC using modular construction. In this example, anintermediate step K pair of nodes in K/2 pairs (e.g., K=4).

The methods, systems and computer program products disclosed hereinprovide interference alignment in a new channel in the form of fullbipartite interference channel (FBIC) where each receiving node sees aninterfering signal from all transmitting nodes. The FBIC channel is apart of the single cell channel (SCC) where the SCC is obtained byaddition of a single node (access point) to the FBIC and considering thebroadcast channel or the downlink channels from the access point to allreceiving points in FBIC and the multiple access channel or the uplinkchannel from all the transmitting points in FBIC to the access point.

In some embodiments, it is considered that uplink CoMP might be harderto realize than the downlink CoMP. Therefore, in some examples, it mightbe desirable not to two adjacent cells to receive in uplink. Forexample, consider a network of three cells with half duplex access pointhaving N antenna each. In such situation, either all three cells are indownlink mode simultaneously or at most one access point is in uplinkmode while the other access points are in uplink mode. However, if theaccess points are full duplex capable, it is enough to have one accesspoint to work in FD mode to receive N−1 in the uplink and transmit Nstreams in the downlink while the other two access point remain in thehalf duplex mode and each transmit N streams in the downlink. It isnoted that it is also possible to change the role of uplink anddownlink, i.e., one access point transmit N−1 streams in downlink whilereceiving N streams in the uplink in full duplex mode while the othertwo access points work in half-duplex mode and each receive N streams inthe uplink. In some examples, a total 4N−1 streams are possible due tomethods described in Lemma 8. In other embodiments, by using all threeaccess points in full duplex mode, it is possible to have differentnumber of uplink streams in the former case or downlink streams in thelatter case that add up to N−1.

Although Lemma 8 characterizes the achievable degrees of freedom and thescaling of

$G_{\frac{FD}{HD}},$

the actual number of nodes in each cell to achieve this gain candrastically change by using different configurations. To this end, wenote that only four nodes are enough to achieve total degree of freedom2N in a single cell while the construction of the lemma requires atleast N users where N is the number of antenna per node. We also notethat the factor of 3N/2 can be achieved in two cells by using theconstruction of Lemma 8. However, the actual bound for possible degreesof freedom in two cells is given by 2N as predicted by the same lemma,although the actual value of 2N is not achievable for any finite N butthe bound is 2N which means that for large enough N we can get as closeas we want to 2N degrees of freedom. For example, if only two cell isdeployed and four nodes per cell are used where each node has N antennathe total degrees of freedom is equal to 8N/6, as depicted in FIG. 13,which corresponds to the gain of 33% in total aggregate downlink anduplink throughput. FIG. 13 depicts the degrees of freedom available in asymmetric (4,4) FBIC with N antennas per node.

FIG. 14 depicts one embodiment of breaking a single FBIC into severalFBIC (not necessarily symmetric with possibly different uplink ordownlink nodes). FIG. 14 depicts one embodiment of the symmetricbreaking of 8 nodes into two FBIC with 4 nodes each with inter-cell andintra-cell interferences.

One result of the methods, systems and computer products disclosedherein is a very optimistic view for the use of full duplex in cellularsystems by analytically proving that the gain of using full duplexaccess point versus using half duplex access point is (1) full 100% in asingle cell (2) considerably maintained over multiple cells having 50%,33%, and 25% for two, three and four cells by algebraic construction,respectively. The actual bound of the gain of using full duplex versushalf duplex access points can be in fact 100%, 50%, and 33% for two,three, and four cells, respectively, and this bound can be achievedthrough solving optimization problem to find out the precoding matrices.Considering the results on local information exchange and sufficiency ofdoing interference alignment locally, there are usually between three tofour base station in each interfering zone and the throughput increasemight remain in upper 30% range.

In another aspect of the present disclosure, a full duplex systemwithout strings is provided to enable full duplex with half duplexclients. Enabling wireless full-duplex (from an AP) with multiplehalf-duplex (HD) clients is key to widespread adoption of full-duplex(FD) in commercial networks. However, enabling FD in such networks isfundamentally challenged by a new form of uplink-downlink interference(UDI), arising between HD clients operating simultaneously in the uplinkand downlink directions of FD. In this context, the present disclosureshows that spatial interference alignment (IA) between clients is aneffective and scalable technique to address UDI and hence enable FD inthese networks, especially in the presence of MIMO. The presentdisclosure also provides a solution and system in the form of FDoS:Full-Duplex without Strings that incorporates this notion.

In one embodiment, FDoS shows that four HD clients can be both necessaryand sufficient to eliminate UDI through IA and enable 2N streams at an Ntransceiver AP. FDoS may also include an efficient MAC design at the APto handle clients with heterogeneous antenna capabilities, maximize thethroughput of the enabled streams in the FD session, as well as reducethe overhead incurred in FDoS, e.g., by half, by facilitating adistributed implementation.

Wireless full-duplex (FD) allows a device to transmit and receive at thesame time in the same frequency band, thereby potentially doubling thelink capacity. However, to allow for widespread adoption of FD, it canbe important to enable FD in commercial networks. In such networks,while the AP can be envisioned to be burdened with additional processingfor FD, it is hard to embed FD functionality in client devices that areenergy constrained to begin with. Hence, in some embodiments, the key towidespread adoption of FD lies in enabling it with half-duplex (HD)clients. Enabling FD with half-duplex clients requires at least twoclients—one for transmitting to the AP, while the other for receivingfrom the AP simultaneously. However, this introduces a new form ofinterference between the uplink and downlink clients of the FD session,which may be referred to as the uplink-downlink interference (UDI, alsocalled inter-node interference).

Towards this challenge of overcoming UDI interference, one ofcontributions of the methods, systems and computer program productsdisclosed herein is showing that spatial interference alignment is apractical and effective approach to addressing the UDI problem infull-duplex both efficiently and scalably. In other words, with multipleantennas being available at the HD clients, uplink (UL) clients canalign their transmissions (interference) towards the downlink (DL)clients in a FD session to eliminate the UDI, as shown in FIGS. 16A and16B, which depict spatial interference alignment. FIG. 16A depictsinterference alignment to address UDI in full duplex (FD) systems. FIG.16B is an interference alignment illustration with a half duplex (HD)client.

To put the proposal of the present disclosure into perspective, notethat for N transceiver AP and client (half-duplex) devices, whileconventional FD systems enable 2N streams only in restricted settings(where UL and DL clients do not interfere or employ side channels) andinterference alignment solutions (for HD systems) are limited to Nstreams, employing spatial interference alignment intelligently withfull-duplex will enable 2N streams without any restriction on the clienttopologies or use of side channels, thereby truly enabling full-duplexin realistic network settings. The FDoS—Full Duplex without Stringssystem disclosed herein incorporates this notion. Several challengesarise in translating this notion into reality.

Specifically, although carried out in the same bandwidth, spatialinterference alignment (IA) requires the estimation of channels betweenthe UL and DL clients. This is an overhead specific to FDoS and scaleswith the number of DL and UL clients involved in the IA process duringthe FD session. In some embodiments, one key result here is in showingthat irrespective of the number of antennas at the AP and clients (sayN), exactly four clients—two in the DL and two in the UL, are necessaryand sufficient to enable 2N streams with FD in any topology. This is aninteresting result in that the additional overhead from IA is fixed(constant), restricted to four additional channel estimations and doesnot depend on N.

While the analytical results indicate the existence of a solution,constructing a feasible solution is a hard problem in itself. As will bediscussed below, the present disclosure provides a low-complexityconstruction in FDoS, that proposes the notion of an interferencealignment network and leverages its structure to generate a feasible IAsolution supporting 2N streams for any given topology. The FDoSdisclosed herein can incorporates a media access control (MAC) design atthe AP that helps maximize the aggregate throughput from the FD session.The role of the MAC can two-fold: (i) compute the IA solution and MIMOprecoders at the clients and AP in an efficient manner to not onlyhandle the UDI problem and enable 2N streams but to also maximize thethroughput of those enabled streams, and (ii) handle clients withheterogeneous antenna capabilities (1≦M≦N) by determining when FD mustbe enabled and how FDoS must be adapted.

The methods, systems and computer program products disclosed hereinleverage spatial interference alignment (IA) in distributed FD networkstowards addressing the UDI problem. Specifically, with multiple antennasbeing available at clients, half-duplex UL clients will use theirspatial dimensions effectively to align their interference (i.e.transmissions to full-duplex AP) towards the half-duplex DL clients in aFD session as shown in FIGS. 16A, 16B. Using the channel stateinformation (CSI) between the UL and DL clients, appropriate precodersat the UL clients and receive filters at DL clients are employed. Thiseliminates the UDI, and hence enable N streams each on both the DL andUL simultaneously (for N antenna devices), thereby securing themultiplexing gain of two from FD. Such an approach has all the desiredattributes of a good solution. (1) Efficient: It operates in the samebandwidth and does not depend on the separation between the UL and DLclients as UDI is addressed explicitly. (2) Scalable: It can secure thedesired multiplexing gain from FD even in the presence of MIMO (i.e.multiple antenna devices) and multiple clients being involved in the FDsession. (3) Deployable: IA, being a form of precoding, is only aschallenging as multi-user MIMO systems and can be realized in practicewith the AP serving as the FD session coordinator.

FIGS. 17A to 17D depict a comparison of interference networks in halfduplex (HD) and full duplex (FD) systems. FIG. 17A depicts a half duplex(HD) interference channel. FIG. 17B depicts a half duplex (HD)communication network. FIG. 17C depicts a full duplex (FD) interferencechannel. FIG. 17D depicts a full duplex (FD) communication network. Oneexample of a T conventional HD interference channel is shown in FIG.17A, where there are K links, each consisting of an M antennatransmitter communicating with an N antenna receiver. In IA theory, theDoF on each of the communication links (di, FIG. 17B) in thisinterference channel essentially correspond to the rank of the precodingmatrices Vi and receive filters Uj such that:

U _(j) H _(ji) V _(i)=0,∀≠j

Rank(U _(j) H _(ji) V _(i))=d _(i) ,∀=j  Equation (32)

Where U_(j) and V_(i) are of size d_(i)×N and M×d, respectively, whileHji is the channel between receiver j and transmitter I and is of sizeN×M. While the first constraint ensures that interfering streams arealigned in the null space of the receivers, the second constraintensures that d_(i) DoFs are available for the desired streams atreceiver of link i. For generic channel matrices H, it has been shownthat it is sufficient to satisfy the first set of constraints (i.e IA),which automatically leads to the second set of constraints beingsatisfied. Based on the above constraints, one can easily obtain thefollowing necessary conditions for a given network to support thedesired DoFs (di, ∀i).

Σ_(i:(i,j)εs) d _(i)(M−d _(i))+Σ_(j:(i,j)εs) ^(d) ^(i) ^(≦min{M,N}) d_(j)(N−d _(j))≧Σ_(i,j:(i,j)εs) d _(i) d _(j)  Equation (33)

where s⊂ε={(i,j); i,jε[1, K]}, the first condition indicates that on alink is limited by the minimum of the number of antennas on either endsof the communication link. The second condition indicates that to have afeasible IA solution, the system defined on any subset (ε) of theinterference constraints (i.e., s) must not be over-constrained. Notethat matrices V_(i) and U_(j) are composed of d_(i) and d_(j) vectorsrespectively. Hence, a single interference constraint in Equation (32)between transmitter i and receiver j is comprised of d_(i) d_(j)equations, while the transmitter and receiver give rise tod_(i)(M−d_(i)) and d_(j)(M−d_(j)) variables respectively. This conditionmay be referred to as the dimension counting argument.

The following description illustrates the principles of FD distributedinterface channel. Referring to FIG. 17A, in the HD interferencechannel, the DoF (number of data streams) are defined on a per-linkbasis, with every receiver (receiving desired streams) being subject tointerference from the transmitters of all the other links. Such aninterference network (graph) captures even FD networks in the peer-peermode. However, the case of distributed FD networks (in a single cell) isquite different for two reasons. (1) Here, all the desired streamseither originate or terminate at a single common node, namely the AP(see FIG. 17D), which does not receive interference from any other nodein the network (other than self-interference during FD, for which weassume ideal suppression). This results in an interference network(called full-duplex interference channel, FDIC) that is fully bipartiteand decoupled from the desired/communication stream network as shown inFIGS. 17C and 17D. (2) Further, with no desired streams going betweenthe nodes in the interference network (i.e. clients), this allows forthe DoF notion to be applied on a per-node basis, with the uplink anddownlink clients potentially operating on different DoF. The IAconstraints for FDIC are as follows:

U _(j) H _(ji) V _(i)=0,∀_(i,j)

Rank(U _(j) H _(j0) V ₀)=d _(j) ^(R),∀_(j)ε{DL clients}

Rank(U ₀ H _(0i) V _(i))=d _(i) ^(T),∀_(j)ε{UL clients}  Equation (35)

where index 0 represents the AP. While the first constraint ensureselimination of interference between “all” pairs of UL and DL clients,the last two constraints allow for varied DoF at each node, with d_(j)^(R) and d_(i) ^(T) being the DoF for the downlink client (receiver)/anduplink client (transmitter) i respectively.

In some embodiments, there can be some necessary conditions for FDIC.With IA in HD and peer-peer FD networks, the goal is to typicallydetermine the maximum DoF that can be achieved over the interferencenetwork. In contrast, with the AP controlling (originating/terminating)all the desired streams in distributed FD networks, the maximum numberof streams that can be enabled by an N transceiver AP is 2N streams. Thenumber of antennas at each client is the same (N) and the aggregatestreams (DoF) are uniformly distributed across the K clients (i.e. p orp+1 DoF at each client, where

${p = \left\lfloor \frac{N}{K} \right\rfloor};$

i.e., N=pK+q; p, qεZ⁺; q<K in either direction as shown in FIG. 18A(clients with asymmetric antennas and DoF on DL and UL are considered inSection 5.4 of the appended article “Full-Duplex without Strings:Enabling Full-Duplex with Half Duplex Clients”). In view of the above,it has been determined that for N antenna HD clients, four clients areneeded for IA to address UDI and enable 2N streams in symmetric FDIC, ifN is even. If N is odd, six clients are needed, which reduces to five(FIG. 17B) in an asymmetric FDIC. This conclusion may be referred to asLemma 10.

It is noted, that the condition on the minimum number of clients is onlya necessary condition, and hence does not guarantee that a feasible IAsolution can be found with four clients. The following provides that thestructure of the interference in symmetric FDIC can be intelligentlyleveraged to construct a feasible IA solution that isimplementation-friendly and can be realized with a small number ofclients. An interference alignment network (IAN) is a subset of theoriginal interference network that captures interference only due totransmit streams that need IA at the receivers. In other words, IANdiscounts those interfering streams that can be suppressed by allocatingan equivalent number of DoF at the receivers (i.e. interferencesuppression), thereby not requiring IA for handling those streams.

FIGS. 19A-19C depict some embodiments of interference alignmentnetworks. FIG. 19A illustrates one embodiment of a full duplex (FD)interference network. In the example depicted in FIG. 19A (with q=0),there are four clients (K=4) each on the DL and UL in FDIC, eachequipped with N=4 antennas (AP has 4 antennas as well) and requires onlya single DoF (p=1) to generate a total of 8 DoF through FD. It is notedthat all interfering streams do not need to be aligned in this examplegiven the requirement of a single DoF with four available dimensions ateach client. Hence, while the interference network is a fully bipartitegraph, as shown in FIG. 18A, the resulting IAN is as shown in FIG. 19B(with K=4). Here, the IAN requires only two of the UL clients' streamsto be aligned (using one DoF) at a DL client, while the other two ULstreams are handled directly through interference suppression (using twoDoF), thereby leaving one DoF for receiving the desired DL stream.

In view of the above, for N antenna HD clients, if the necessaryconditions are satisfied, there exists a feasible IAN with at most one(un-directed) cycle that can enable 2N streams in symmetric FDIC. Theproof is by means of providing a construction for a feasible IAsolution.

IAN Construction: For example, to provide an IAN construction, insymmetric FDIC, q clients desire to send or receive p+1 streams, whilethe remaining K−q clients desire p streams. The necessary conditionshave been shown to be satisfied for this interference network. Thefollowing IAN with a single cycle involving 2K clients as shown in FIG.19C can now be constructed. There are three types of DL clients: (i) qof them requiring p+1 streams and receiving interference from 2(p+1)streams from two UL clients; (ii) K−q−1 of them requiring p streams andreceiving interference from 2p streams from two UL clients; and (iii)one DL client requiring p streams and receiving interference from 2p+1streams from two UL clients.

Feasibility: Consider a DL client requiring p+1 streams. d_(IA)=p+1dimensions are used to align interference from a net 2(p+1) streams fromthe two UL clients (edges in IAN). Further, (K−2) edges, i.e. (K−q)edges with p streams each and (q−2) edges with p+1 streams each, areremoved at the DL client (compared to interference network). Thisrequires that d_(IS)=(K−q)p+(q−2)(p+1) dimensions are set aside at theclient to handle these streams through interference suppression. Thiseventually leaves N−d_(IA)−d_(IS)=p+1 remaining dimensions, which issufficient to handle the desired (p+1) streams at the client. Similarly,the desired streams at the other types of DL clients can also be shownto be supported by this IAN. Hence, the IAN is feasible and can support2N streams through FD.

IA Solution: The construction is as follows. The individual IAconditions for this IAN can be given separately for the cyclic (top 2qnodes) and the non-cyclic (bottom 2(K−q) nodes) part as,

H _(ii) V _(i)

H _(ik) V _(k) ,∀iε[1,q],k=(i+1)(mod)_(q)  Equation (36)

H _(ii) V _(i)

H _(ik) V _(k) ,∀iε[q+1,K],k=(i+1)(mod)K  Equation (37)

Substituting back in the cyclic component provides:

V ₁

(Π_(i−=q) ¹ H _(ik) ⁻¹ H _(ii))V ₁ ,k=(i+1)(mod)q  Equation (38)

Thus, V₁ can be composed of any p+1 Eigen vectors of the matrix Π_(i−=q)¹H_(ik) ⁻¹H_(ii) to provide the required N×(p+1) matrix. The rest of theprecoding matrixes in the cycle (V_(i), iε[2, q]) can be computedsequentially from the first set of constraints in Equation (37).

Since, the second set of constraints couple the rest of the precodingmatrices (Vi, iε[q+1,K]) to V₁ through DL client K (i.e. V_(K)), once V₁is computed, they can be determined as well. However, these K−qprecoding matrices are N×p in size compared to V1 that is N×(p+1) insize. Therefore, first V_(K) is obtained as an N×(p+1) precoding matrixfrom V_(K)=H_(K1) ¹H_(KK)V₁. Since only p streams are transmitted by theUL clientK, p is picked out of the p+1 vectors in V_(K) to make it N×pin size.

Thereafter, the remaining precoding matrices Vi, iε[q+1,K−1] of size N×pcan be sequentially obtained from V_(K) from the second set ofconstraints in Equations (36) and (37).

The corresponding receiver filters (U_(i)) of dimensions N×(p+1) or N×pare obtained orthogonal to the sub-space spanned by H_(ii)V_(i). WhenN=K_(p), i.e. q=0, the IAN consists of a single Hamiltonian cycle, withall clients requiring the same streams as shown in FIG. 19B. Thissimplifies the solution to only the cyclic part of the generic N=K_(p)+qcase, and would require only the first step of the construction, albeitapplied over all the clients.

Since symmetric FDIC automatically results in IANs with at most a singlecycle, this indicates that a feasible IA solution exists for thenetworks disclosed herein. Hence, the necessary conditions for IA insymmetric FDIC also serve as sufficient conditions.

FDoS solution: While a feasible IA can be constructed for any symmetricFDIC with 2K clients, to minimize the overhead of CSI from IA, thepresent solution enables FD with exactly four clients (two DL and two ULclients) with N 2 streams each. This is the smallest number of clientsneeded to realize 2N streams when N is even (here q=0). The IAconstruction is as follows.

(i) V₁ is composed of

$\frac{N}{2}$

eigen vectors of the N×N matrix to result in N×N/2 precoding matrix forUL client 1.(ii) V2 is again a N×N/2 precoding matrix for UL client 2 that is givenby V₂=^(s)H₁₂ ⁻¹H₁₁V₁.(iii) From V₁ and V₂, the N/2 dimensional receiver filters for the twoDL clients, namely U₁ and U₂ (matrices of size

$\frac{N}{2}$

×N) are obtained orthogonal to the sub-space spanned by H₁₁V₁ and H₂₂V₂respectively.

Similarly, when N is odd, our construction would require six clients(K=3) and would follow the appropriate procedure described above withrespect to sections titled IAN constructions, feasibility, and IAsolution, depending on whether N is a multiple of 3 or not. FIGS. 20Aand 20B illustrates the IAN and IA construction pictorially for N=4 andN=5 respectively, wherein N is the number of antenna. In FIG. 20A thereare 8 signal streams and in FIG. 20B there are 10 signal streams.

We now outline one embodiment of the complete sequence of steps inexecuting an FD session in FDoS with reference to FIG. 21. (1) Decide FDvs. HD: Based on desired scheduling/QoS policies (proportional fairnessin our case), the four clients for a FD session in FDoS are chosen bythe AP. Based on the number of antennas available at the clients, thetotal number of streams possible through FD can be determined using theinstructions provided in Section 5.4 of the appended article“Full-Duplex without Strings: Enabling Full-Duplex with Half DuplexClients”, and compared against N streams possible with HD. FD is enabledonly if it can enable a larger number of streams (than in HD).

(2) Channel Estimation and Feedback: Once FD is chosen, the clients inthe session are notified. The channels between AP and the four clientsas well as between the clients themselves are estimated, followed by theintelligent (reduced) feedback procedure as outlined in Section 5.3 ofthe appended article “Full-Duplex without Strings: Enabling Full-Duplexwith Half Duplex Clients”.

(3) Distributed Computation of Solution: In addition to determining itsown precoder and receive filter, the AP disseminates the precoder forone of the UL clients. Using this, the rest of the precoder and receiverfilters are computed locally at each of the clients, in accordance withSections 5.2 and 5.3 of the appended article “Full-Duplex withoutStrings: Enabling Full-Duplex with Half Duplex Clients”.

(4) Executing FD Session: The FD session is then enabled by the APbetween the four clients in the symmetric (2M or 2N streams) orasymmetric (M+N streams) mode as appropriate. The AP serves as the pointcoordinator (e.g., cellular BS, PCF mode in 802.11) for the FD session.

(5) ACK Delivery: The delivery of ACKs follows a procedure similar todownlink MU-MIMO operation 802.11ac, wherein the AP solicits block ACKs(BA) from each of the MU-MIMO clients (except the first client)sequentially. In one example, in addition to a block ACK request (BAR)for the second DL client, the AP also needs to send back two ACKs to thetwo UL clients. This can be achieved by piggybacking the two ACKs forthe UL clients onto the ACK-request for the second DL client as shown inFIG. 21, thereby not having to incur additional transmissions.

In another aspect of the present disclosure, a system for providingfull-duplex communication in a wireless network is provided, as depictedin the block diagram this is provided by FIG. 22. The system forproviding full-duplex communication in a wireless network includes amodule for transmission of signals to a plurality of receiving usersthrough a full duplex network 902, a module for receiving signals from aplurality of transmitting users from a full duplex network 903, and amodule for aligning the transmission of the transmitting users at thereceiving users.

In one embodiment, the system 900 preferably includes one or moreprocessors 918, e.g., hardware processor, and memory 916 for storingapplications, modules and other data. In one example, the one or moreprocessors 918 and memory 916 may be components of a computer, in whichthe memory may be random access memory (RAM), a program memory(preferably a writable read-only memory (ROM) such as a flash ROM) or acombination thereof. The computer may also include an input/output (I/O)controller coupled by a CPU bus. The computer may optionally include ahard drive controller, which is coupled to a hard disk and CPU bus. Harddisk may be used for storing application programs, such as someembodiments of the present disclosure, and data. Alternatively,application programs may be stored in RAM or ROM. I/O controller iscoupled by means of an I/O bus to an I/O interface. I/O interfacereceives and transmits data in analog or digital form over communicationlinks such as a serial link, local area network, wireless link, andparallel link.

The system 900 may include one or more displays 914 for viewing. Thedisplays 914 may permit a user to interact with the system 900 and itscomponents and functions. This may be further facilitated by a userinterface 920, which may include a mouse, joystick, or any otherperipheral or control to permit user interaction with the system 900and/or its devices, and may be further facilitated by a controller 915.It should be understood that the components and functions of the system900 may be integrated into one or more systems or workstations. Thedisplay 914, a keyboard and a pointing device (mouse) may also beconnected to I/O bus of the computer. Alternatively, separateconnections (separate buses) may be used for I/O interface, display,keyboard and pointing device. Programmable processing system may bepreprogrammed or it may be programmed (and reprogrammed) by downloadinga program from another source (e.g., a floppy disk, CD-ROM, or anothercomputer).

The system 900 may receive input data 906 which may be employed as inputto a plurality of modules 905 that provide the module for the long termbattery management layer 902 for estimating and managing a life cyclefor the battery, and the module for the real time power management layer904 for managing power sharing between the at least one battery storageelement and the at least one capacitor storage element. The system 900may produce output data 922, which in one embodiment may be displayed onone or more display devices 514. It should be noted that while the aboveconfiguration is illustratively depicted, it is contemplated that othersorts of configurations may also be employed according to the presentprinciples.

Further details regarding the functionality of the modules 902, 903, 904for the simultaneous full duplex transmission and reception of signalsby a plurality of receiving and transmitting users across a wirelessnetwork, as well as the alignment, e.g., interference alignment, of thetransmission signal at the receiving users, has been provided above withreference to FIGS. 1-20. In some embodiments, the system furtherincludes at least one cell channel comprising an access point node, anda full bipartite interference channel (FBIC) configuration of aplurality of receiving nodes and a plurality of transmitting nodes. Insome embodiments, each receiving node receives an interfering signalfrom all transmitting nodes, and the access point node of the cellchannel provides a single node having downlink channels to all receivingnodes in the FBIC, wherein all of the uplink channels from the FBIC areto the single access point node to the single cell channel. Removing theinterfering signal transmitted through the full bipartite interferencechannel (FBIC) configuration removes interference via interferencealignment.

Embodiment 2

The main challenge in deployment of full duplex systems in a network isthe scaling of the promised doubling of the spectral efficiency by thefull duplex operation when multi-user communication and multiple antennasystems are considered. This invention addresses a practical way ofsolving this challenge in a wireless system consisting of a single cellor multiple cells with a full duplex access points. The users in thecell might or might not be full duplex capable.

Some prior art have identified this problem without properly addressingit. In some prior art it is proposed to use imbalance mode of operationwhen the number of uplink users are usually much lower than the numberof downlink users. Some work has looked into the possibility ofselecting users that generate the list interference on other users forexample through geo tagging or feedback of the channel states betweenthe users. Some other work have considered the possibility of using agenie channel or in practical sense having another frequency band orchannel that is not used in the actual communication to providefeedforward or feedback between nodes for the purpose of interferencecancellation.

We propose interference alignment where all the uplink nodes try toalign their interferences only on a subset of resolvable degrees offreedom of each downlink user. This technique has been considered inother context, e.g., in interference channel, relay channel, orX-channel while the channel of the single cell is different and requiresa different treatment and eventually has different type of solution.

At the current moment and with the present knowledge in the state of theart, the full duplex systems would not work in a network or it has verylimited use unless the proposed technique is deployed. Nonetheless,there might be future progress and work that can address this problem ina different way or by enhancing our proposed scheme.

A key feature is the interference alignment:

-   -   Using interference alignment in full duplex single cell systems.    -   Using interference alignment in multi-cell full duplex systems.    -   Using only four nodes per cell.    -   Two nodes may be in the uplink and two nodes may be in the        downlink.

The new and different solution is required for interference alignment inthe single cell channel (SCC) which is composed of a full bipartiteinterference channel (FBIC) between the users in the cell and abroadcast channel from the access point to the downlink users and amultiple access channel from the uplink users to the access point.

Embodiment 3

Enabling wireless full-duplex (from an AP) with multiple half-duplex(HD) clients is key to widespread adoption of full-duplex (FD) incommercial networks. However, enabling FD in such networks isfundamentally challenged by a new form of uplink-downlink interference(UDI), arising between HD clients operating simultaneously in the uplinkand downlink directions of FD. In this context, we first show thatspatial interference alignment (IA) between clients is an effective andscalable technique to address UDI and hence enable FD in these networks,especially in the presence of MIMO. We then present our solution andsystem FDoS: Full-Duplex without Strings that incorporates this notion.We build the theory of applying spatial IA to full-duplex networks ingeneral and present elegant, implementation-friendly constructions forgenerating feasible IA solutions that leverage the structure ofinterference specific to these networks. In the process, FDoS shows thatfour HD clients are both necessary and sufficient to eliminate UDIthrough IA and enable 2N streams at an N transceiver AP. FDoS alsoincludes an efficient MAC design at the AP to handle clients withheterogeneous antenna capabilities, maximize the throughput of theenabled streams in the FD session as well as reduce the overheadincurred in FDoS by half by facilitating a distributed implementation. Aprototype of FDoS on WARP radios showcases its ability to address UDIand hence enable 2N streams in varied settings with just four HDclients.

1. Introduction

Wireless full-duplex (FD) allows a device to transmit and receive at thesame time in the same frequency band, thereby potentially doubling thelink capacity. Although promising, one of the key challenges inrealizing full-duplex is the Self-Interference (SI) generated by the Txantenna at the Rx antenna on the device, which can be several orders ofmagnitude stronger than the received signal from a desired node. Severalresearch works have looked at addressing this SI problem in the analogdomain through antenna [7, 10, 1] and RF cancellation [16, 12, 8, 4]techniques, as well as through digital cancellation [12, 8] schemes.

With the focus being on addressing the SI problem, current works havelooked at FD from a peer-peer standpoint, with both nodes of the linkbeing FD enabled. However, to allow for widespread adoption of FD, it isimportant to enable FD in commercial networks. In such networks, whilethe AP can be envisioned to be burdened with additional processing forFD, it is hard to embed FD functionality in client devices that areenergy constrained to begin with. Hence, the key to widespread adoptionof FD lies in enabling it with half-duplex (HD) clients.

Enabling FD with half-duplex clients requires at least two clients—onefor transmitting to the AP, while the other for receiving from the APsimultaneously. However, this introduces a new form of interferencebetween the uplink and downlink clients of the FD session as shown inFIG. 23( a). We refer to this interference that is specific to FDcommunication as the uplink-downlink interference (UDI, also calledinter-node interference [3, 17]). There are two simple, but practicalapproaches to addressing UDI with HD clients. (1) Leverage ClientSeparation: Separating the UL and DL clients of the FD session as faraway as possible is one option to alleviate UDI. However, [1] showedthat this significantly reduces the opportunities for FD in a cell andreduces the gains from FD to as low as 20-30% even in the presence ofideal SI cancellation. (2) Use of Side-channel: With most client devicesbeing equipped with both 3G/4G and WiFi interfaces, it is possible tosend a coded version of the interfering packet from the UL client to theDL client through a side (orthogonal) channel (e.g. WiFi interface),while the primary channel (e.g. 3G/4G) is being used for FDcommunication (e.g. [3]). This would allow the DL client to partially orcompletely remove the UDI on its primary channel as shown in FIG. 23(b). However, such a solution comes at the expense of additionalbandwidth, which when accounted for, diminishes the gains from FD.Further, both these approaches do not scale to multi-stream FD (i.e. FDwith MIMO). Hence, the focus of this work is to address the UDI problemarising in full-duplex with half-duplex clients efficiently using thesame bandwidth and allowing it to scale to multi-stream FD (i.e. FD withMIMO) transmissions.

Towards this challenge, one of our main contributions in this work is inshowing that spatial interference alignment is a practical and effectiveapproach to addressing the UDI problem in full-duplex both efficientlyand scalably. In other words, with multiple antennas being available atthe HD clients, UL clients can align their transmissions (interference)towards the DL clients in a FD session to eliminate the UDI as shown inFIG. 24( a). To put our proposal in perspective, note that for Ntransceiver AP and client (half-duplex) devices, while conventional FDsystems enable 2N streams only in restricted settings (where UL and DLclients do not interfere or employ side channels) and interferencealignment solutions (for HD systems) are limited to N streams, employingspatial interference alignment intelligently with full-duplex willenable 2N streams without any restriction on the client topologies oruse of side channels, thereby truly enabling full-duplex in realisticnetwork settings.

We present our solution and system, FDoS—Full Duplex without Strings,which incorporates this notion. Several challenges arise in translatingthis notion into reality.

(1) Specifically, although carried out in the same bandwidth, spatialinterference alignment (IA) requires the estimation of channels betweenthe UL and DL clients. This is an overhead specific to FDoS and scaleswith the number of DL and UL clients involved in the IA process duringthe FD session. Our key result here is in showing that irrespective ofthe number of antennas at the AP and clients (say N), exactly fourclients—two in the DL and two in the UL, are necessary and sufficient toenable 2N streams with FD in any topology. This is an interesting resultin that the additional overhead from IA is fixed (constant), restrictedto four additional channel estimations and does not depend on N. This isin contrast to the results for HD systems [5, 11], where 2(N−1) streamsare possible with IA alone, but the overhead scales with N2 (N ifclients can receive from multiple transmitters [11]).

(2) While the analytical result only indicates the existence of asolution, constructing a feasible solution is a hard problem in itself.Here, we present a low-complexity construction in FDoS, that proposesthe notion of an interference alignment network and leverages itsstructure to generate a feasible IA solution supporting 2N streams forany given topology. (3) In translating our solution from data streams toactual throughput, FDoS incorporates a MAC design at the AP that helpsmaximize the aggregate throughput from the FD session. The role of theMAC is two-fold: (i) compute the IA solution and MIMO precoders at theclients and AP in an efficient manner to not only handle the UDI problemand enable 2N streams but to also maximize the throughput of thoseenabled streams, and (ii) handle clients with heterogeneous antennacapabilities (1≦M≦N) by determining when FD must be enabled and how FDoSmust be adapted. (4) Finally, our solution lends itself naturally to adistributed implementation across clients. This is leveraged by FDoSthrough intelligent feedback mechanisms to further reduce the overheadincurred in executing our solution by half.

We prototype FDoS using the WARP software-defined radio platform. Whilethe AP is enabled with full-duplex, the clients are restricted to behalf-duplex.

Our contributions in this work are multi-fold:

-   -   We show that spatial interference alignment is an effective        approach to address the UDI problem in FD communication and        build the theory and design behind its application.    -   We propose our solution and system FDoS, which shows that four        clients are both necessary and sufficient to enable 2N streams        in FD with the help of IA and present an elegant construction to        realize such a solution in reality.    -   We design an efficient MAC to handle clients with heterogeneous        antenna capabilities, maximize the throughput of the enabled        streams in the FD session and reduce the additional (albeit        constant) overhead incurred in FDoS by half through a        distributed implementation.    -   We build a prototype of FDoS with WARP radios and showcase its        ability to enable 2N streams in most topologies in practice with        just four clients.

2. Background

2.1 Full-Duplex

Full-duplex networks can be of two types: peer-peer and distributed. Inpeer-peer, both the nodes of a FD link are FD enabled and ischaracteristic of relay and backhaul networks. On the other hand, indistributed FD networks, only the AP is FD enabled, while the clientsdevices are half-duplex. This is characteristic of practical wirelessnetworks (e.g. WLANs), where one can expect to burden the AP withadditional (FD) processing, while the clients are legacy half-duplexdevices that are energy constrained. The focus of this work is ondistributed FD networks, which unlike its peer-peer counterpart, requireat least two clients to enable a FD session—one that transmits to theAP, while the other simultaneously receives from the AP as shown in FIG.23( a). Such a configuration results in a new form of interferencecreated by the uplink client on the downlink client during the FDsession. We refer to this interference that is unique to distributed FDnetworks, as the uplink-downlink interference (UDI), which forms acritical challenge towards realizing FD in practical networks.

2.2 Interference Alignment

IA allows more interfering streams to be accommodated in lesser resourcedimensions, thereby leaving room to accommodate more desired streams.While the resource dimensions can correspond to those in time, frequency(called frequency or symbol extension) or space (antennas), our focus inthis work is on spatial IA. The latter allows for a practicalrealization in MIMO systems, unlike the former approaches that byrelying on certain non-practical channel assumptions (e.g. non-causalCSI), serve mainly as theoretical constructs. The example in FIG. 24( b)illustrates spatial IA. Three APs with two antennas each, desire to senda single data stream to its respective client, each with two antennas.Being limited to two antennas (two spatial dimensions) at the clientsand assuming no transmitter cooperation, only two of the streams can bedelivered in this network without IA. However, with IA all three streamscan be delivered. The two interfering streams at each of the clients canbe aligned to consume a single spatial dimension (degree of freedom,DoF), thereby allowing the other dimension for its desired stream. Thealignment in turn is realized through a process known as precoding,whereby the data stream (d) at the transmitter is multiplied by aprecoding vector (_v) before being transmitted through the antennas ontothe channel such that

H _(ji) {right arrow over (v)} _(i)

H _(jk) {right arrow over (v)} _(k) ,∀j,s.t. j≠i≠k  (a1)

where H_(ji) is the channel matrix between transmitter i and receiver j,and

indicates that the span of the vector spaces defined by matrices oneither sides of the operator are the same. The precoders at thedifferent transmitters are chosen based on the above constraints torealize the desired alignment, while the receive filters at thereceivers are chosen orthogonal to the space of the interference toreceive the desired streams.

2.3 Related Work

Interference Alignment (IA):

The notion of interference alignment was introduced in [6]. In general,characterizing the maximum number of streams that can be supported andrealized through IA in interference channels has been an elusive problemand has been considered under various network settings in thecommunications literature (see [13, 2] and references therein).Recently, [5] showed that in an interference channel with K links, witheach node of the link having N antennas each, one can potentiallyachieve 2N streams asymptotically (as K→∞) with IA alone. In thenetworking space, IA has been leveraged along with transmittercooperation (packet sharing) to generate 2N streams on the uplink and2N−2 streams on the downlink. A distributed version of the scheme waslater proposed in [14].

Further, [15] considered the realization of blink IA in practice. Notethat the above results are for half-duplex systems. As we will showlater, interestingly, the interference channel generated by thedistributed FD network is different from that in the HD network andhence warrants a fresh understanding of the applicability of IA in FD.

Full Duplex (FD):

The bulk of the system works on FD have focused on addressingself-interference through antenna [7, 10, 1], RF [16, 9, 12, 8, 4,] anddigital [9, 12, 8, 4,] cancellation. Recently, [20] tried to effectivelyleverage exposed terminals along with FD transmissions in a network. Thefocus of these works has been on the peer-peer FD model. The importanceof distributed FD with HD clients and hence the need to address UDI wasonly recently considered in [3]. The focus of [3] has been toinformation-theoretically characterize the benefits of having aside-channel to distributed FD in a three-node, two stream FD network.The cost of the side-channel as well as scalability to multiple streamsin FD (i.e. MIMO in either direction of FD) was not considered.

FD+IA:

Very recently, [17] proposed the use of IA in the time domain (throughsymbol extension) for addressing UDI in FD networks, albeit with FDcapability at both the AP and (single-antenna) clients. The focus of[17] is characterizing DoF from an information-theoretic perspective.Being based on time alignment, it requires either non-causal CSI orinterference to deterministically repeat itself (in future) to eliminateUDI and is not conducive for a practical realization.

Our focus in this work is to propose and leverage spatial IA as apractical, bandwidth-efficient and scalable approach to address the UDIproblem and hence enable full-duplex in distributed FD networks with HDclients. More importantly, we intend to develop the theory and designbehind applying IA in these networks, while also addressing thechallenges that arise in realizing a practical system.

3. Case for IA in FD

3.1 Significance of UDI

To understand its impact, we conduct numerical as well as channeltrace-based simulation (testbed details in Section 7) of a simple 3 nodedistributed FD network as shown in FIG. 23( a). In reality, the impactof UDI depends on the specific clients chosen on the uplink and downlinkdirections for the FD session, which in turn depends on a variety of MACrelated factors such as the set of active clients available in theuplink and downlink, their local channel status (busy/idle), queueoccupancy, scheduling policies, etc. To account for these variations, wevary the position of the uplink and downlink clients to create severaltopologies and measure the SNR at the downlink client both in thepresence and absence of the uplink client. The difference between theseSNRs provides an estimate of the impact of the UDI. It can be seen fromthe CDF in FIG. 25 that UDI creates about x dB of interference at thedownlink clients in a large fraction of topologies, leaving little roomfor leveraging client separation. This significantly diminishes theopportunities and hence gains from full-duplex as pointed out in [1].Further, this restriction on topology would only be increased when MIMO(multiple streams) is enabled from different clients in both the UL andDL directions—one has to now remove UDI between multiple pairs of UL andDL clients simultaneously (as seen in FIG. 24).

3.2 Interference Alignment for UDI

We propose to leverage spatial interference alignment (IA) indistributed FD networks towards addressing the UDI problem. In the restof this paper, IA refers to spatial IA. Specifically, with multipleantennas being available at clients, (half-duplex) UL clients will usetheir spatial dimensions effectively to align their interference (i.e.transmissions to full-duplex AP) towards the (half-duplex) DL clients ina FD session as shown in FIG. 24. Using the channel state information(CSI) between the UL and DL clients, appropriate precoders (at ULclients) and receive filters (at DL clients) will be designed. Thiswould eliminate the UDI and hence enable N streams each on both the DLand UL simultaneously (for N antenna devices), thereby securing themultiplexing gain of two from FD.

3.3 Challenges

As with any closed-loop MIMO system, by relying on CSI, our solution isapplicable to clients whose channels have coherence times reasonableenough to amortize the overhead of CSI estimation. Note that withclosed-loop MIMO becoming mainstream (multi-user MIMO in 802.11ac), thislimitation would be imposed on any FD or HD system that employsclosed-loop MIMO (even in the absence of IA).

Specific to our approach though, there arise several key challenges intranslating our vision into a practical solution.

Performance:

The ability to generate 2N streams and hence a multiplexing gain of two(g=2) from FD, has a direct correspondence to capacity only in the highSNR regime [6],

C(SNR)=g log(SNR)+o(log(SNR))  (a2)

In reality, different choices of precoders and receive filters at theclients, will result in different rates (throughput) for the desiredstreams to (from) the AP, although they may all eliminate the UDIbetween the clients. Hence, it is important to compute the IA solutionand hence MIMO precoders and filters at the clients and AP in anefficient manner to not only handle the UDI problem and enable 2Nstreams but to also maximize the throughput of those enabled streams.

Overhead:

Although our solution operates in the same bandwidth, it requires CSIfor channels between the UL and DL clients, which constitutes additionaloverhead over that incurred by baseline closed-loop, HD MIMO systemsbetween the AP and clients. Further, this overhead would scale with thenumber of clients needed on the DL and UL to address the UDI problem inFD through IA. Hence, it is important to address the UDI with the leastamount of additional overhead. This would include not only determiningthe minimum number of clients needed for the FD session, but alsoreducing the CSI overhead incurred by the chosen clients for the IAprocess.

Handling Heterogeneity:

In practical settings, client devices may possess lesser number ofantennas than the AP. Further, the number of antennas on the device canvary across clients. For example, smartphones and tablets may be limitedto two antennas, while laptops, desktops and smart TVs can potentiallyhouse more antennas. Hence, it is important to understand how theperformance of our approach will be impacted by such heterogeneity andhow to adapt to the same.

Towards addressing these challenges, we present our solution and system,FDoS—Full-Duplex without Strings, that enables full duplex indistributed multi-stream (MIMO) FD networks without relying on sidechannels, client separation or non-causal CSI. We first present ouranalytical results on leveraging IA in distributed FD networks in thenext section, followed by the design components of FDoS that handle allthe practical challenges in Section 5.

4. IA in Distributed FD Networks

4.1 Primer on IA Theory

Consider the conventional HD interference channel as shown in FIG. 26(a), where there are K links, each consisting of an M antenna transmittercommunicating with an N antenna receiver. The DoF on each of the HDcommunication links (d_(i), FIG. 26( b)) essentially correspond to therank of the precoding matrices V_(i) and receive filters U_(j) such that[20]

U _(j) H _(ji) V _(i)=0,∀i≠j

Rank(U _(i) H _(ii) V _(i))=d _(i) ,∀i=j  (a3)

where U_(j) and V_(i) are of size d_(i)×N and M×d_(i) respectively,while H_(ji) is the channel between receiver j and transmitter i and isof size N×M. While the first constraint ensures that interfering streamsare aligned in the null space of the receivers, the second constraintensures that d_(i) DoFs are available for the desired (communication)streams at the receiver of link i. For generic channel matrices H, it issufficient to satisfy the first set of constraints (i.e. IA), whichautomatically leads to the second set being satisfied [20].

Necessary Conditions:

Based on the above constraints, one can easily obtain the followingnecessary conditions [20] for a given network to support the desiredDoFs (d_(i), ∀i):

d _(i)≦min{M,N}

d _(i)(M−d _(i))+

d _(j)(N−d _(j))≧

d _(i) d _(j)  (a4)

where

⊂

={(i,j); i,jε[1, K]}. The first condition indicates that the DoF on alink is limited by the minimum of the number of antennas on either endsof the communication link. The second condition indicates that to have afeasible IA solution, the system defined on any subset (

) of the interference constraints (i.e.

) must not be over-constrained. Note that matrices V_(i) and U_(j) arecomposed of d_(i) and d_(j) vectors respectively. Hence, a singleinterference constraint in Eqn. 2 between transmitter i and receiver jis comprised of d_(i)d_(j) equations, while each transmitter andreceiver gives rise to d_(i)(M−d_(i)) and d_(j)(N−d_(j)) variablesrespectively [20]. We refer to this condition as the dimension countingargument.

4.2 Distributed FD Interference Channel

In the HD interference channel (FIG. 26( a)), the DoF (used synonymouslywith number of data streams) are defined on a per-link basis, with everyreceiver (receiving desired streams) being subject to interference fromthe transmitters of the other links. Such an interference network(graph) captures even FD networks in the peer-peer mode. However, thecase of distributed FD networks (i.e. in a single cell) is quitedifferent for two reasons. (1) Here, all the desired streams eitheroriginate or terminate at a single common node, namely the AP (see FIG.26( d)), which does not receive interference from any other node in thenetwork (other than self-interference during FD, for which we assumeideal suppression in analysis). This results in an interference network(called full-duplex interference channel, FDIC) that is fully bipartiteand decoupled from the desired/communication stream network as shown inFIGS. 26( c) and 26(d). (2) Further, with no desired streams exchangedbetween the nodes in the interference network (i.e. clients), thisallows for the DoF notion to be applied on a per-node basis, with theuplink and downlink clients potentially operating on different DoF.Thus, the IA constraints for FDIC are as follows:

U _(j) H _(ji) V _(i)=0,∀i,j

Rank(U _(j) H _(j0) V ₀)=d _(j) ^(R) ,∀jε{DL clients}

Rank(U ₀ H _(0i) V _(i))=d _(i) ^(T) ,∀iε{UL clients}

where, index 0 represents the AP. While the first constraint ensureselimination of interference between “all” pairs of UL and DL clients,the last two constraints allow for varied DoF at each node, with d_(j)^(R) and d_(i) ^(T) being the DoF for the downlink client (receiver) jand uplink client (transmitter) i respectively. As we will showsubsequently (Section 3.6), the unique nature of interference indistributed FD networks, makes IA much more valuable in these networksthan in HD networks.

4.3 Necessary Conditions for FDIC

With IA in HD and peer-peer FD networks, the goal is to typicallydetermine the maximum DoF that can be achieved over the interferencenetwork. In contrast, with the AP controlling (originating/terminating)all the desired streams in distributed FD networks, the maximum numberof streams that can be enabled in a single cell by an N transceiver APis 2N streams. We assume N antennas are sufficient to generate 2Nstreams in FD [4]. However, our results and solution apply even ifadditional antennas (e.g. 2N [7]) are needed. Hence, we are interestedin the alternate question: how many clients are needed for the IAsolution to help address the UDI problem and help realize the 2N streamsin FD? Answering this question will help us understand how to controlthe overhead incurred from IA (due to additional CSI estimation) in oursolution. Further, given N antenna HD clients and a limit of N streamsin either direction in FD, we are primarily interested in enabling 2Nstreams in symmetric FDIC. Here, the number of antennas at each clientis the same (N) and the aggregate 2N streams (DoF) are uniformlydistributed across the K clients in either direction as shown in FIG.27( a) (i.e. p or p+1 streams at each client, where

$\left. {{{p = \left\lfloor \frac{N}{K} \right\rfloor};{{i.e.\mspace{14mu} N} = {{pK} + q}};p},{{q \in ^{+}};{q < K}}} \right).$

Clients with asymmetric antennas and DoF on DL and UL are considered inSection 4.4. We now have the following encouraging result:

Lemma 1 For N antenna HD clients, only four clients are necessary for IAto enable 2N streams in symmetric FDIC, if N is even. If N is odd, sixclients are necessary, which reduces to five (FIG. 27( b)) in anasymmetric FDIC.

Proof We first consider the case of N being even. With an upper bound ofN DoF in either direction of FD, we consider K clients each on the DLand UL such that the N DoF are divided uniformly among the K clientswith q clients obtaining p+1 DoF and the remaining K−q clients obtainingp DoF (where

$\left. {{N = {{pK} + q}},p,{{q \in };{p = \left\lfloor \frac{N}{K} \right\rfloor};{q < K}}} \right).$

With two types of clients (requiring p or p+1 DoF) in either direction,we have four types of interference pairs between clients, resulting inthe following number of interference constraints (equation):

$\begin{matrix}{{ɛ} = {{{{p\left( {p + 1} \right)}\left( {K - q} \right)q} + {\left( {p = 1} \right)^{2}q^{2}} + {p^{2}\left( {K - q} \right)}^{2} + {{p\left( {p + 1} \right)}\left( {K - q} \right)q}} = {\left( {{\left( {p + 1} \right)q} + {p\left( {K - 1} \right)}} \right) = N^{2}}}} & ({a6})\end{matrix}$

Counting the number of variables per client, we obtain the aggregatenumber of variables (A) as,

A = (p + 1)(N − p − 1)2q + p(N − p)2(K − q) = 2N² − 2 Np − 2q(p + 1)  %  on  simplification

Now, for the dimension counting argument to hold, we need A≧|ε|, i.e.

2N ²−2Np−2q(p+1)≧N ²

Applying N=pK+q and simplifying, the constraint reduces to,

K(K−2)p ²+2(K−2)pq+q(q−2)≧0  (a7)

When N is even, the above constraint holds for K≧2 (where q=0 when K=2).However, when N is odd, K=2 results in q=1, which does not satisfy theconstraint. However, with K≧3, the constraint is satisfied for N beingodd.

Thus, when N is even, we need at least two clients on both DL and UL(four in total) to remove UDI through IA and hence enable 2N streams.One might wonder if assuming an asymmetric number of clients on DL andUL can help realize 2N streams with lesser clients. Note that with threeclients, one of the directions has a single client that mustsend/receive N streams, thereby becoming the bottleneck for IA. Hence 2Nstreams is not possible with three clients. Further, there is no notionof IA for two clients.

When N is odd, we need at least three clients in either direction (sixin total) for the symmetric FDIC. However, with an asymmetric set-up,five clients may be sufficient with three clients in only one of thedirections as shown in FIG. 27( b). Specifically, we have the number ofvariables

$\left( {{4\left\lfloor \frac{N}{2} \right\rfloor^{2}} + {6\left\lfloor \frac{N}{2} \right\rfloor}} \right)$

to be greater than the number of equations

$\left( {{4\left\lfloor \frac{N}{2} \right\rfloor^{2}} + {4\left\lfloor \frac{N}{2} \right\rfloor} + 1} \right)$

in this case.

4.4 Constructing a Feasible Solution

Note that the condition on the minimum number of clients is only anecessary condition and hence does not guarantee that a feasible IAsolution can be found with four clients. Indeed the problem ofconstructing feasible IA solutions for maximizing the number of streamsis a challenging one even in HD networks, where algebraic solutions areavailable only for small scale networks [5]. In contrast, for ourdesired objective of eliminating UDI to enable 2N streams, we show thatthe structure of interference in symmetric FDIC can be intelligentlyleveraged to construct a generic IA solution. Further, the solution isimplementation-friendly, applies to general topologies and can berealized with a small number of clients. First, we introduce thefollowing definition:

Definition 1 An interference alignment network (IAN) is a subset of theoriginal interference network that captures interference only due totransmit streams that need IA at the receivers.

In other words, IAN discounts those interfering streams that can besuppressed by allocating an equivalent number of DoF at the receivers(i.e. interference suppression), thereby not requiring IA for handlingthose streams. In the example in FIG. 28( a) (with q=0), say, we havefour clients (K=4) each on the DL and UL in FDIC, each equipped with N=4antennas (AP has 4 antennas as well) and transmits/receives only asingle stream (p=1) to generate a total of 8 streams through FD. Notethat all interfering streams do not need to be aligned in this examplegiven the requirement of a single stream with four available dimensions(4 DoF) at each client. Hence, while the interference network is a fullybipartite graph as shown in FIG. 28( a), the resulting IAN is as shownin FIG. 28( b) (with K=4). Here, the IAN requires only two of the ULclients' streams to be aligned (using one DoF) at a DL client, while theother two UL streams are handled directly through interferencesuppression (using two DoF), thereby leaving behind one DoF forreceiving the desired DL stream.

Lemma 2 For N antenna HD clients, if the necessary conditions aresatisfied, there exists a feasible IAN with at most one (un-directed)cycle that can enable 2N streams in symmetric FDIC.

The proof is by means of providing a construction for a feasible IAsolution.

IAN Construction:

In symmetric FDIC, q clients require to send or receive p+1 streams,while the remaining K−q clients require p streams. The necessaryconditions have been shown to be satisfied for this interference networkearlier. We now construct the following IAN with a single un-directedcycle involving 2K clients as shown in FIG. 28( c). This IAN has threetypes of DL clients: (i) q of them receiving p+1 desired streams andinterference from 2(p+1) streams from two UL clients; (ii) K−q−1 of themreceiving p streams and interference from 2p streams from two ULclients; and (iii) one DL client receiving p streams and interferencefrom 2p+1 streams from two UL clients.

Feasibility:

Consider a DL client receiving p+1 desired streams. d_(IA)=p+1dimensions are used to align interference from a net 2(p+1) streams fromthe two UL clients (two edges in IAN). Further, (K−2) edges, i.e. (K−q)edges with p streams each and (q−2) edges with p+1 streams each, areremoved at the DL client (compared to original interference network).This requires that d_(IS)=(K−q)p+(q−2)(p+1) dimensions are set aside atthe client to handle these streams through interference suppression.This eventually leaves N−d_(IA)−d_(IS)=p+1 remaining dimensions, whichis sufficient to receive the desired (p+1) streams at the client.Similarly, the desired streams at the other types of DL clients can alsobe shown to be supported by this IAN. Hence, the IAN is feasible and cansupport 2N streams through FD.

IA Solution:

The construction is as follows: The individual IA conditions for thisIAN can be given separately for the cyclic (top 2g nodes) and thenon-cyclic (bottom 2(K−q) nodes) part as,

H _(ii) V _(i)

H _(ik) V _(k) ,∀iε[1,q],k=(i+1)(mod)q  (a8)

H _(ii) V _(i)

H _(ik) V _(k) ,∀iε[q+1,K],k=(i+1)(mod)K

Substituting back in the cyclic part, we get,

V ₁

(Π_(i=q) ¹ H _(ik) _(i) ⁻¹ H _(ii))V ₁ ,k _(i)=(i+1)(mod)q  (a9)

(i) Thus, V₁ can be composed of any p+1 Eigen vectors of the matrixΠ_(i=q) ¹H_(ik) _(i) ⁻¹H_(ii) to provide the required N×(p+1) matrix.The rest of the precoding matrices in the cycle (V_(i), iε[2, q]) canthen be computed sequentially from the first set of constraints in Eqns.7.

(ii) Since, the second set of constraints couple the rest of theprecoding matrices (V_(i), iε[q+1, K]) to V₁ through DL client K (i.e.V_(K)), once V₁ is computed, they can be determined as well. However,these K−q precoding matrices are N×p in size compared to V₁ that isN×(p+1) in size. Hence, we first obtain V_(K) as an N×(p+1) precodingmatrix from V_(K)=H_(K1) ⁻¹H_(KK)V_(i). Since only p streams aretransmitted by the UL client K, we then pick p out of the p+1 vectors inV_(K) to make it N×p in size.

(iii) Thereafter, the remaining precoding matrices V_(i),iε[q+1, K−1] ofsize N×p can be sequentially obtained from V_(K) from the second set ofconstraints in Eqns. 7.

(iv) The corresponding receive filters (U_(i)) of dimensions N×(p+1) orN×p are obtained orthogonal to the sub-space spanned by H_(ii)V_(i).

When N=Kp, i.e. q=0, the IAN consists of a single Hamiltonian cycle,with all clients requiring the same p streams as shown in FIG. 28( b).This simplifies the solution to only the cyclic part of the genericN=Kp+q case, and would require only the first step of the construction,albeit applied over all the clients.

COROLLARY 1. The necessary conditions in Eqns. 4 are also sufficient fora symmetric FDIC.

Since symmetric FDIC automatically results in IANs with at most a singlecycle, this indicates that a feasible IA solution always exists forthese networks. Hence, the necessary conditions for IA in symmetric FDICalso serve as sufficient conditions.

4.5 FDoS Solution

While we can construct a feasible IA solution for any symmetric FDICwith 2K clients, to minimize the overhead of CSI from IA, our solutionenables FD with exactly four clients (two DL and two UL clients) with

$\frac{N}{2}$

streams each. Recall that this is the smallest number of clients neededto realize 2N streams when N is even (here q=0). The IA construction isas follows:

(i) V₁ is composed of

$\frac{N}{2}$

Eigen vectors of the N×N matrix H₂₁ ⁻¹H₂₂H₁₂ ⁻¹H₁₁ to result in

$N \times \frac{N}{2}$

precoding matrix for UL client 1.

(ii) V₂ is again a

$N \times \frac{N}{2}$

precoding matrix for UL client 2 that is given by V₂

H₁₂ ⁻¹H₁₁V₁.

(iii) From V₁ and V₂, the

$\frac{N}{2}$

dimensional receive filters for the two DL clients, namely U₁ and U₂(matrices of size

$\frac{N}{2} \times N$

) are obtained orthogonal to the sub-space spanned by H₁₁V₁ and H₂₂V₂respectively.

Similarly, when N is odd, our construction would require six clients(K=3) and would follow the appropriate procedure in Section 3.4depending on whether N is a multiple of 3 or not. FIG. 29 illustratesthe IAN and IA construction pictorially for N=4 and N=5 respectively.

4.6 the Result in Perspective

To put our result in perspective, we consider two relevant and recentresults from IA in the spatial (MIMO) domain for HD systems [5, 11].Recently, [5] showed that in a HD MIMO interference channel with Kcommunication links containing N antenna nodes, one can potentiallyachieve

$\frac{2\; {NK}}{K + 1}$

streams, i.e. 2(N−1) streams (when K=N−1) with IA alone, while requiringO(N²) transceivers and O(N²) CSI estimations of N×N links. When clientsare allowed to receive from multiple APs, [11] showed that 2(N−1)streams are possible with IA alone, but with N−1 APs and two clients,thereby requiring O(N) CSI estimations and O(N²) transceivers. Incontrast, we have shown that IA in FD systems can help generate 2Nstreams with O(N) transceivers and just four HD clients (and one FD AP),restricting the CSI estimations to just 8 links (4 with respect to AP,and 4 between clients) that is independent of N. One can attribute thisinteresting result specifically to the structure of FDIC, wherein halfthe interfering streams are those that are generated by the AP (intendedfor DL clients), which are automatically available for self-interferencecancellation during its reception of half the desired streams (from ULclients). Hence, IA is needed only for the other half of theinterference streams that are generated by the UL clients on the DLclients.

Another interesting point to note is that in HD systems, one can scalethe number of concurrent streams (with number of APs) or equivalentlyachieve 2N streams with lesser number of APs by allowing for APcooperation (i.e sharing data streams between APs, e.g. network MIMO).However, the role of IA vanishes in such scenarios, where APcooperation/processing handles all the interference between APs. Incontrast, even if APs are allowed to cooperate, the UDI problem (beingspecific to clients) will continue to pose a challenge for FD systems.Hence, we believe that IA plays a key role in handling the UDI problemin FD networks. Further, the nature of FDIC, makes IA an ideal solutionto address UDI and enable 2N streams in an efficient manner (with low,fixed overhead) with just four HD clients.

5 FDoS: Design Components

We now present the various MAC layer design components that aim toleverage our results from the previous section to build a practicalsolution for FD with half-duplex clients in a single cell.

5.1 Client Selection

In any closed-loop MIMO transmission from/to an AP (e.g. multi-userMIMO), the net rate (throughput) depends on the channels of the set ofclients (and their mutual interference) involved in the transmission. Ifthe CSI is available for all clients, then the best subset of clientscan be selected for the transmission. However, collecting the CSIestimates not only constitutes overhead but also incurs latency, whichcould render the CSI estimates invalid/stale (depending on the channelcoherence time) during operation. For this reason, 802.11ac decouplesclient selection from the MU-MIMO transmission process—clients are firstchosen based on QoS/scheduling policies, CSI is estimated only for thechosen clients, and then MU-MIMO transmission is optimized (throughprecoding) for the chosen clients. In the case of FD with IA, the rateof the FD session not only depends on individual client channels withrespect to AP but also on the channels between the clients. The latteramplifies the CSI estimation problem in FD systems with IA, therebyprompting us to decouple client selection from precoder optimization ina manner similar to 802.11 ac systems.

5.2 Maximizing Throughput

While our solution from Section 3 eliminates the UDI between the chosenclients through IA, it does not directly contribute to improving thethroughput of the desired streams. Hence, once the four clients (two onDL and two on UL) are chosen by the AP scheduler based onpriorities/weights, queue occupancy, etc. (we pick proportionalfairness), FDoS focuses on optimizing the rate of the FD session for thechosen set of clients.

Recall that in addition to the precoders and receive filters at theclients, we also need to design a precoder and receive filter for the AP(V₀, U₀). The core problem to address is as follows: we need toconstruct precoders (V_(i)) at the UL clients and the receive filter atthe AP (U₀) for the UL streams, while also constructing the precoder(V₀) at the AP and the receive filters (U_(j)) at the DL clients for theDL streams in FD. These two MU-MIMO problems in both directions arecoupled through the interference between the UL and DL streams at the APas well as the DL clients. While the former is addressed throughself-interference cancellation, the latter is addressed through IA.Here, we assume ideal self-interference cancellation.

FDoS adopts a modular approach to determining the precoders and receiverfilters for the AP and clients through a two-step procedure as follows:Since the UDI problem is responsible for coupling the two MU-MIMOproblems, FDoS first determines the IA solution for UDI (Section 3).Then, leveraging the flexibility of the precoders and receive filtersalready designed at the clients from the IA process, FDoS optimizes thereceive filter and precoder at the AP in the UL and DL directions tomaximize the rate of the UL and DL streams respectively. The key stepsare as follows:

(1) Optimize the precoders (V₁ and V₂) at the UL clients and receivefilter (U₀) at the AP to maximize the rate of the UL streams. Note that,the design of V₁ (to remove UDI) allows the flexibility of picking

$\frac{N}{2}$

eigen vectors (out of N) of the matrix H₂₁ ⁻¹H₂₂H₁₂ ⁻¹H₁₁. These

$\frac{N}{2}$

vectors that form V₁ are chosen appropriately to maximize the rate ofthe N UL streams to the AP as follows:

-   -   Let V_(1′)=[{right arrow over (v)}₁₁{right arrow over (v)}₁₂ . .        . {right arrow over (v)}_(1N)]. For every {right arrow over        (v)}_(1i), the corresponding vector in V_(2′) is given as {right        arrow over (v)}_(2i)=H₁₂ ⁻¹H₁₁{right arrow over (v)}_(1i). Pair        the eigen vectors from V_(1′) and V_(2′) as {({right arrow over        (v)}_(1i), {right arrow over (v)}_(2i))}, ∀iε[1,N].    -   Compute the rate metric for the UL streams corresponding to        every pair of their eigen vectors as,

R _(i,UL)=Rate({right arrow over (u)} _(0i) ¹ H ₀₁ ^(U) {right arrowover (v)} _(1i))+Rate({right arrow over (u)} _(0i) ² H ₀₂ ^(U) {rightarrow over (v)} _(2i))  (a10)

where {right arrow over (u)}_(0i) ¹ and {right arrow over (u)}_(0i) ²are the receive filter vectors (e.g. LMMSE filters) at the AP (total ofN vectors) corresponding to the precoding vectors at UL clients 1 and 2respectively. Given {right arrow over (v)}_(1i) and {right arrow over(v)}_(2i), {right arrow over (u)}_(0i) ¹ and {right arrow over (u)}_(0i)² can be easily computed to maximize the individual rate terms in theabove equation. We employ the Shannon formula for the rate function[19].

-   -   Arrange the pair of eigen vectors in descending order of their        uplink rate metric. Then, pick the top

$\frac{N}{2}$

pairs to construct the corresponding precoding matrices V₁ and V₂ ofsize

$N \times \frac{N}{2}$

for the two UL clients. Similarly, use the corresponding

$\frac{N}{2}$

receive filter vectors ({right arrow over (u)}_(0i) ¹,{right arrow over(u)}_(0i) ²) (computed above) for the AP to construct the

$\frac{N}{2} \times N$

receive filter matrices U₀ ¹ and U₀ ², and hence its final N×N receivefilter matrix U₀=[U₀ ¹ ^(T) U₀ ² ^(T) ]^(T).

(2) Compute receive filters (U₁ and U₂) for DL clients to remove UDI.Given V₁ and V₂, the receive filters U₁ and U₂ of size

$\frac{N}{2} \times N$

at DL clients 1 and 2 are obtained orthogonal to the sub-space spannedby H₁₁V₁ and H₂₂V₂ respectively, wherein the interference from both ULclients have been aligned.

(3) Determine the precoding matrix (V₀) for the AP to maximize the rateof the DL streams. Having computed the receive filters U₁ and U₂ basedon IA, the precoding matrix for the AP V₀ is computed to maximize therate of the N downlink streams,

R _(DL)=Rate(U ₁ H ₁₀ ^(D) V ₀ ¹)+Rate(U ₂ H ₂₀ ^(D) V ₀ ²)  (a11)

where V₀ ¹ and V₀ ² are the two

$N \times \frac{N}{2}$

precoding matrices with respect to the two DL clients, that togetherform the N×N precoding matrix V₀ at the AP, i.e. V₀=[V₀ ¹V₀ ²].

Note that FDoS optimizes the UL precoders first. However, one could alsostart by optimizing the DL precoders. While one can envision to jointlyaddress the UL and DL MU-MIMO problems (along with IA) through a verycomplex optimization problem, this will not favor implementation. Incontrast, we will now show how our modular approach allows for adistributed implementation, thereby reducing overhead.

5.3 Reducing Overhead

A straight-forward implementation of the above solution will consist ofthe following steps:

(i) AP sends pilots for channel estimation at DL clients, followed by ULclients 1 and 2 for channel estimation at the AP (H₀₁ ^(U), H₀₂ ^(U)) aswell as at the DL clients.

(ii) DL clients 1 and 2 estimate and feedback DL CSI H₁₀ ^(D) and H₂₀^(D) respectively to the AP.

(iii) In addition, DL client 1 estimates and feeds back UL-DL CSI H₁₁and H₁₂ to the AP for IA. Similarly, DL client 2 feeds back H₂₁ and H₂₂to the AP.

(iv) With all the required CSI, the AP computes all the desiredprecoders and receive filters, V₀, V₁, V₂, U₀, U₁, U₂. AP then transmitsV₁, V₂ to the UL clients, which the DL clients overhear and use tocompute their own receive filters U₁ and U₂.

Note that the transmission of pilots from the AP (step 1) and feedbackof CSI from the DL clients (step 2) are common to a HD MU-MIMO(downlink) system. However, the pilots from the UL clients (step 1),feedback of inter-client CSI (step 3) and precoders for the UL clients(step 4) are specific to our FD system, thereby constituting additional(albeit fixed) overhead. With the pilots constituting negligibleoverhead relative to the CSI and precoder feedback, the bulk of theoverhead is incurred in steps 3 and 4.

We propose an alternate approach that leverages the distributed natureof our solution to reduce the overhead incurred by half. While steps 1and 2 are the same, the remaining steps are as follows:

(iii) DL client 1 feeds back only H₁₂ ⁻¹H₁₁ to AP for IA. Similarly, DLclient 2 to feeds back only H₂₁ ⁻¹H₂₂ to AP.

(iv) AP then transmits only V₁ to the UL clients, which UL client 2 andDL clients use to compute their precoder V₂ and receiver filters U₁, U₂respectively.

Thus, the overhead of four N×N CSI matrices and two

$N \times \frac{N}{2}$

precoder matrices is reduced to two N×N CSI matrices and a single

$N \times \frac{N}{2}$

precoder matrix, brining about an overhead reduction of half

We now show how the above approach with reduced feedback information issufficient to execute our entire solution. Note that the aggregated CSIinformation provided by the DL clients is sufficient for the AP toexecute Step 1 of our Algorithm in Section 4.2 and hence obtain V₁, V₂,U₀. The AP then provides only V₁ as feedback to the UL and DL clients.UL client 2 uses this information along with H₁₂ ⁻¹H₁₁ (overhead duringfeed back from DL client 1) to compute its own precoder V₂ locally as inStep 1, i.e. V₂=H₁₂ ⁻¹H₁₁V₁. Similarly, DL clients 1 and 2 also locallycompute V₂. Now, with access to both V₁ and V₂ and their local CSI, i.e.(H₁₁, H₁₂) for DL client 1 and (H₂₁, H₂₂) for DL client 2, both the DLclients can compute their respective receive filters U₁ and U₂ locallyas in Step 2. The AP also has all the necessary information to computethe same receive filters U₁ and U₂ that will be used at the DL clientsand hence its corresponding precoder V₀ as in Step 3.

5.4 Handling Heterogeneity

In reality, one might encounter scenarios, where clients have variednumber of antennas. We consider such cases to understand when and howFDoS and more generally full-duplex can be applied.

Case 1: All clients have M=1 antenna—Although the AP has N antennas, ifthe HD clients are all restricted to a single antenna, no spatial IA ispossible. Hence, UDI will have to be addressed by relying on clientseparation, side channels [3], etc. However, it is hard to scale suchapproaches from single stream (in either direction) to MIMO FD systems.Consequently, it might be beneficial to operate the system inhalf-duplex in such cases (especially for large N), where MU-MIMO can beapplied to generate N streams in a single direction.

Case 2: All clients have M (1<M≦N) antennas—Here IA is possible and FDoScan be applied to deliver 2M streams in FD. However, depending on how 2Mcompares to N, one still needs to decide whether to operate the systemin FD or HD.

Case 3: Some clients have M (1<M≦N) antennas and others have Nantennas—This is a practical scenario that can arise often. For e.g.smartphones/tablets with two antennas and laptops, smart TVs with moreantennas. We show that the performance of FDoS is not restricted byclients with lesser antennas (i.e. 2M streams), but provides a gracefulperformance (M+N streams) utilizing all the available antennas in thesystem effectively.

Theorem 1 FDoS delivers M+N streams with four HD clients, two each withM and N antennas respectively (M, N being even).

PROOF. We provide a proof for the case that M and N are both evenintegers. Without loss of generality let us assume that M≦N. We use thefollowing construction to achieve M+N streams: Each of two clients withM antennas as the UL clients transmit

$\frac{M}{2}$

desired streams to the AP on UL and the other two clients with Nantennas serve as the DL clients receiving

$\frac{M}{2}$

streams each from the AP on the DL. Thus, there are M streams on the ULinterfering with N streams on the DL.

Based on the dimension counting argument, the number of variables

$\frac{N^{2} + M^{2}}{2}$

is greater than the number of interference constraints MN. Hence, thenecessary conditions are satisfied for this topology.

In the following we provide a construction that shows that in fact it ispossible to have DoF per node that is half of the number of antennas ateach node. First we note that the precoders and receiver filters at eachnode denote a subspace of the vector space defined by the number ofantennas at each node. At a transmitter node this vector space is usedfor the transmission and at a receiver node this space is free ofinterference from the transmission performed in the uplink and can beused for reception of the signal from AP. If we have two vector spacesof size Min the uplink their image in each of the receiver node has anintersection that is of size 2M−N if the channels between the uplink anddownlink nodes are generic. In order to find this intersection weconsider the channels from the uplink nodes to a downlink node, e.g.,H₁₂ and H₁₁. Let us denote the column of these two matrices by h₁, . . ., h_(M) and g₁, . . . , g_(M), respectively. The matrix A=[h₁, . . . ,h_(M), g₁, . . . , g_(N-M)] is full rank by the assumption of thechannels being generic. Therefore, we can write the 2M−N vectorsg_(N-M+1), . . . , g_(M) in terms of the columns of A, e.g.,

$\begin{matrix}{g_{N - M + k} = {{\sum\limits_{i = 1}^{M}\; {\alpha_{1}^{k}h_{i}}} + {\sum\limits_{i = 1}^{N - M}\; {\beta_{1}^{k}g_{i}}}}} & ({a12})\end{matrix}$

By rearranging the above equation we find the vectors that are in theintersection of the images of the transmit vector spaces at thisreceiver. We have the following:

$\begin{matrix}{w_{k} = {{\sum\limits_{i = 1}^{M}\; {\alpha_{1}^{k}h_{i}}} = {g_{N - M + k} - {\sum\limits_{i = 1}^{N - M}\; {\beta_{1}^{k}g_{i}}}}}} & ({a13})\end{matrix}$

Under the condition of the channel being generic, it can be shown thatthe collection of the vectors w_(k) generates a full rank matrix C=[w₁,. . . , w_(2M−N)]. The inverse image of the matrix C in the vectorspaces of the two transmitting nodes defines the subspaces thatintersect at the receiver node and we denote them by C₁ and C₂ for thetwo transmitting nodes 1 and 2, respectively. We call these vectorspaces the common vector spaces. The orthogonal subspaces with thesevector spaces at the transmitting nodes 1 and 2 and the receiving pointare called the disjoint vector spaces and denoted by D₁, D₂ and D,respectively.

The property of these vector spaces is as follows:

(1) For generic channel condition, the size of C is N×(2M N),

(2) For generic channel condition, the size of C₁ and C₂ is equal toM×(2M−N),

(3) For generic channel condition, the size of D is N×2(N−M),

(4) For generic channel condition, the size of D₁ and D₂ is equal toM×(N−M),

(5) Any precoding vector that lies in the spaces defined by D_(i) or D₂will be received in the spaces defined by D,

(6) Any precoding vector that lies in the spaces defined by C_(i) or C₂will be received in the spaces defined by C,

(7) Any two streams transmitted from two transmitters by using twoprecoding vector that lies in the spaces defined by D₁ and D₂,respectively, will be received in disjoint subspaces of the vectorspaces defined by D,

(8) Any streams received in a vector space that lies within the vectorspace defined by C can be mapped to a transmission that has happenedfrom either transmitting node 1 or 2 where the precoding matrix definesa subspace of the vector space D₁ or D₂, respectively.

Given the above property, it is simple to see that the disjoint vectorspaces do not require any interference alignment and we can freelychoose any subspace of size

$\frac{N - M}{2}$

at me transmitter and they will take away at most

$2*\frac{N - M}{2}$

at each of the receiving nodes. On the other hand, in the common vectorspaces, one can apply the same construction used for the symmetric FDICto generate additional

$\frac{{2\; M} - N}{2}$

degrees of freedom per node.

5.5 Putting it all Together

We now outline the complete sequence of steps in executing an FD sessionin FDoS (see FIG. 30 for illustration).

(1) Decide FD vs. HD: Based on desired scheduling/QoS policies(proportional fairness in our case), the four clients for a FD sessionin FDoS are chosen by the AP. Based on the number of antennas availableat the clients, the total number of streams possible through FD isdetermined (Section 5.4) and compared against N streams possible withHD. FD is enabled only if it can enable a larger number of streams (thanin HD). Scheduling decisions can also incorporate information on numberof client antennas.

(2) Channel Estimation and Feedback: Once FD is chosen, the clients inthe session are notified. The channels between AP and the four clientsas well as between the clients themselves are estimated, followed by theintelligent (reduced) feedback procedure as outlined in Section 5.3.

(3) Distributed Computation of Solution: In addition to determining itsown precoder and receive filter, the AP disseminates the precoder forone of the UL clients. Using this, the rest of the precoder and receiverfilters are computed locally at each of the clients (Sections 5.2, 5.3).

(4) Executing FD Session: The FD session is then enabled by the APbetween the four clients in the symmetric (2M or 2N streams) orasymmetric (M+N streams) mode as appropriate. The AP serves as the pointcoordinator (e.g. cellular BS, PCF mode in 802.11) for the FD session.

(5) ACK Delivery: The delivery of ACKs follows a procedure similar todownlink MU-MIMO operation 802.11ac, wherein the AP solicits block ACKs(BA) from each of the MU-MIMO clients (except the first client)sequentially. In our case, in addition to a block ACK request (BAR) forthe second DL client, the AP also needs to send back two ACKs to the twoUL clients. This is achieved by piggybacking the two ACKs for the ULclients onto the ACK-request for the second DL client as shown in FIG.30, thereby not having to incur additional transmissions.

6. Implementation

We prototype FDoS using WARPLab in a 6-node WARP testbed that uses acombination of v2 and v3 WARP boards. We use a 802.11-compatible 10 MHzOFDM PHY with 64 sub-carriers for UL and DL transmissions. The keyimplementation details are as follows:

Full Duplex. We implement a simple 2-antenna MIMO full-duplex platform(similar to MIDU [1]) for the FD AP. We employ two WARP nodes for theAP, one for transmission and other for reception simultaneously, andsynchronize their clocks. Our platform achieves up to a 28 dB of analogsignal cancellation over a 1 MHz OFDM channel. Note that the impact ofUDI is independent of the amount of self-interference (SI) cancelled atthe FD node. Even though our FD implementation does not sufficientlycancel all self-interference, it suffices to illustrate the benefitsthat can be achieved by eliminating UDI using FDoS. Further, one canemploy more sophisticated techniques for SI cancellation as well [4].

Antenna Configuration.

We evaluate FDoS under homogeneous and heterogeneous antennaconfigurations. Under the homogenous setting, each HD (UL, DL) and FD(AP) node has either 2 or 4 antennas. Under the heterogeneousconfiguration, UL and FD nodes have 4 antennas while DL nodes have only2 antennas. These configurations are representative of real-worldwireless networks: mobile devices (e.g. tablets and cellphones) can beexpected to have up to 2 antennas while larger devices (e.g. laptops,desktops) can easily hold 4 or more.

Clock Synchronization.

While it is convenient to maintain clock and phase synchronizationbetween all nodes in a testbed via a wired back-channel, such anapproach may not be realistic in all scenarios. Current wireless devicescannot be expected to have such fine-grained clock synchronization.Hence, we do not maintain wired clock synchronization between our nodes.Our experiments will show that FDoS will still be able to eliminate UDIunder such conditions.

CSI Measurement.

We measure all UL and DL CSI using separate probe packets. The precodersand receiver filters computed from these CSIs based on FDoS's design arethen used in subsequent data frames. Due to the high latency involved inWARPLab, the delay between the CSI measurements and data transmissionsis larger than that found in typical WiFi transmissions. Even so, FDoScan eliminate a significant fraction of UDI under such conditions ofhigh CSI variability. This points the fact that FDoS can eliminate UDIeven under realistic mobility found in real-world networks.

7. Performance Evaluation

7.1 Set-up

Test-Bed:

The experiments are conducted in a typical indoor office environment.Two WARP nodes jointly serve as the FD AP, while the remaining fournodes serve as four HD clients. The WARP radio boards/antennas aredistributed throughout this environment to create different topologies.Our results are averaged over several topologies as well as overmultiple runs.

Baselines and Metrics:

We evaluate FDoS against two baselines: (i) FDoS without the IAcomponents, i.e. DL and UL operate independently without alleviatingtheir mutual interference, and (ii) a half-duplex MU-MIMO systememploying conventional ZFBF for its DL and UL. CSI are estimated on eachof the 64 sub-carriers precoding is carried out on a sub-carrier basisin our experiments. Since the CSI cannot be ensured to be static acrossdifferent schemes, each of our experiment involves sending about500-1000 frames back-back to generate enough samples for a confidentcomparison. We use SINR measured from the experiments as our primarymetric and translate it to rate using the Shannon capacity formulawherever appropriate.

7.2 Benchmarking IA

We first evaluate the performance of the IA delivered by FDoS inpractice. We consider both a 2 and 4 antenna setup, wherein all nodesare equipped with 2 and 4 antennas respectively, and generate 2 and 4streams respectively on the UL and DL simultaneously. The impact of FDoSin alleviating UDI during FD is captured in FIG. 31. It can be seen thatFDoS provides a large UDI suppression of about 15-20 dB in the 2 antennacase even without any clock sync between the nodes. In the 4 antennacase, the lack of clock sync FDoS's has a larger impact and limits theUDI suppression in FDoS to 10 dB, which is still promising to enableeffective communication on the DL as we will see in the rate results.This clearly indicates FDoS's ability to handle UDI effectively, andhence enable 2N streams (4 and 8 streams in our experiments) in adistributed FD network.

7.3 FDoS Performance

We now evaluate FDoS by measuring the performance delivered to the DLstreams in the presence of UDI (FIG. 32) and the resulting net rate(FIGS. 32, 34(a), and 34(b)). The UL clients operate at 3-5 dB lowerpower than the FD AP node. FIG. 32 presents the CDF (over topologies andruns) of the DL SINR (averaged over the streams). FIG. 32( a) shows thatUDI can significantly hurt performance in the 2 antenna case, bringingdown the median HD SINR (i.e. without any UDI) by about 30 dB. It isvery promising that FDoS can suppress almost 20 dB of the UDI to sufferonly a 10 dB loss in SINR, which would be more than compensated by theadditional streams that it enables on the downlink. In the 4 antennacase in FIG. 32( b), lack of clock sync limits median UDI suppression to10 dB, which turns out to be sufficient to still provide a FD gain overHD as we show subsequently.

We present the rate results in FIGS. 34( a) and 34(b) as a function ofincreasing transmit power on the UL clients. Several observations can bemade: (i) The aggregate HD MU-MIMO rate does not scale well for the 4antenna case (compared to the 2 antenna case).

8. Conclusions

We consider and address the challenging problem of uplink-downlinkinterference (UDI) in distributed FD networks by leveraging spatialinterference alignment in an efficient, practical and scalable manner.We build the theory and design of applying IA to distributed FD networksand show that four HD clients are sufficient to enable the multiplexinggain of two possible with FD. We present our system FDoS that leveragesthe structure of interference in these networks to construct elegant IAsolutions, while incorporating several MAC layer design elements totranslate our solution into reality. A prototype evaluation of FDoSusing WARP radios shows significant promise for FDoS in addressing UDIand truly enabling FD with HD clients.

Embodiment 4

Enabling wireless full-duplex (from an AP) with multiple half-duplex(HD) clients is key to widespread adoption of full-duplex (FD) incommercial networks. However, enabling FD in such networks isfundamentally challenged by a new form of uplink-downlink interference(UDI), arising between HD clients operating simultaneously in the uplinkand downlink directions of FD. In this context, we first show thatspatial interference alignment (IA) between clients is an effective andscalable technique to address UDI and hence enable FD in these networks,especially in the presence of MIMO.

The bulk of the system works on FD have focused on addressingself-interference through antenna, RF and digital cancellation. Somerecent work has tried to effectively leverage exposed terminals alongwith FD transmissions in a network. The focus of these works has been onthe peer-peer FD model. The importance of distributed FD with HD clientsand hence the need to address UDI was only recently considered in [3].The focus of [3] has been to information-theoretically characterize thebenefits of having a side-channel to distributed FD in a three-node, twostream FD network. The cost of the side-channel as well as scalabilityto multiple streams in FD (i.e. MIMO in either direction of FD) was notconsidered. FD+IA: some work have proposed the use of IA in the timedomain (through symbol extension) for addressing UDI in FD networks,albeit with FD capability at both the AP and (single-antenna) clients.The focus of these work is characterizing DoF from aninformation-theoretic perspective. Being based on time alignment, itrequires either non-causal CSI or interference to deterministicallyrepeat itself (in future) to eliminate UDI and is not conducive for apractical realization. Our focus in this work is to propose and leveragespatial IA as a practical, bandwidth-efficient and scalable approach toaddress the UDI problem and hence enable full-duplex in distributed FDnetworks with HD clients. More importantly, we intend to develop thetheory and design behind applying IA in these networks, while alsoaddressing the challenges that arise in realizing a practical system.

We then present our solution and system FDoS: Full-Duplex withoutStrings that incorporates this notion. We build the theory of applyingspatial IA to full-duplex networks in general and present elegant,implementation-friendly constructions for generating feasible IAsolutions that leverage the structure of interference specific to thesenetworks. In the process, FDoS shows that four HD clients are bothnecessary and sufficient to eliminate UDI through IA and enable 2Nstreams at an N transceiver AP. FDoS also includes an efficient MACdesign at the AP to handle clients with heterogeneous antennacapabilities, maximize the throughput of the enabled streams in the FDsession as well as reduce the overhead incurred in FDoS by half byfacilitating a distributed implementation.

Our solution can be used to scale the full duplex gain in multi-userscenario. The current work on full duplex communication lack areasonable solution in multi-user systems, e.g., cellular systems andour solution is the first and most efficient known scheme to date.

A key idea of the invention is to realize full duplex communicationbetween multiple users that are in the same interference domain. Thisfeature allows the gain of full duplex technology to scale with theincreasing number of users. The above key feature is realized through aninterference alignment that is the enabling feature. There are severalnovel ideas related to this enabling feature that can be categorizedinto:

(1) Finding the number of streams and scheduling clients based on theirchannels and number of antennas that can be used in the full duplexsystem and interference alignment between them is possible.

(2) Constructing a solution for interference alignment problem byfinding linear precoder and linear receiver filters that can be used insuccession with other processing at the transmitter and receiver.

-   -   Constructing low complexity and algebraic solutions for        interference alignment in a bipartite network wherein nodes are        divided into two sets (1) the transmitting nodes and (2) the        receiving nodes.    -   Generating interference alignment solution by using uplink        downlink duality.    -   Providing an interference alignment in multiple nodes by using        the idea of generating loops in the connecting graph of the        network.

(3) Providing a means and simplified feedback and feedforward signalingwhich enables interference alignment in a typical system. Alsooptimizing the estimation, feedback, and feedforward overhead.

(4) Optimizing the transmission rate (in the downlink) and receptionrate (in the uplink) in conjunction with the interference alignmentsolution.

-   -   Selecting a partial number of virtual antennas or interference        free dimensions (degrees of freedom per node) in order to        optimize the rate with respect to selecting a precoder that        belong to a subspace of the space defined by the degrees of        freedom per node.    -   Selecting the best interference alignment solution out of a        finite set of solutions (where the solution set of interference        alignment problem has finite number of solutions) that maximizes        the throughput in the network (or partial throughput, e.g., the        uplink throughput or the downlink throughput).    -   Optimizing the precoders e.g., to maximize the throughput or a        capacity measure (based on joint decoding or stream by stream        decoding, e.g., by using MMSE filters for each streams) when the        solution set of the interference alignment problem has infinite        solutions.

(5) Using a novel concept of degrees of freedom per node.

-   -   Defining virtual antennas at each node based on the degrees of        freedom per node.    -   Defining the precoders and receiver filters that correspond to a        set of virtual antennas at each node.

(6) Providing techniques to deal with communication problem in a networkin two steps. First step to define an interference network where thesources of interference in the network and their effect on receivers areconsidered and the interference is mitigated though interferencealignment. The result of the first step is a simplified network in whichthe interference links are removed and the network of the desiredchannel between the communication node is updated with transformedchannel characteristics and updated number of antennas (or virtualantennas) at each node. The second step is to address the communicationproblem in a network in which the interference (or part of interference)is removed.

An aspect includes a method of interference management between two setsof communication points comprising a set of communication pointconsisting at least one communication point that are transmitting asignal, a second set of communication point consisting at least onecommunication point that are receiving data, a transmitting node employsvirtual antennas for transmissions, a receiving node employs virtualantennas for reception, wherein, the signal of each antenna is obtainedthrough linear processing of the signals at virtual antennas. Thereceived signal at a virtual antenna of a receiving node may notaffected by the transmission from virtual antennas at a transmittingnode. The linear processing may be used to minimize the received signalpower at a virtual antenna of a receiving node when a transmitting nodeis active.

Another aspect includes a method of mitigating interference received ata downlink user from the uplink transmission in order to achieve fullduplex uplink and downlink communication between an access point and aplurality of user equipments. The interference may be mitigated by usingprecoding at the transmitting nodes. The interference may be mitigatedby using receiver filters at the receiving nodes. The precoder andreceiver filters may be designed to minimize the interference at thereceiving node from the transmitting nodes.

Still another aspect includes a method of interference mitigationcomprising interference alignment in common signal dimension. Commonsignal dimension may be defined in spatial dimension.

Still another aspect includes a method of interference mitigationcomprising interference alignment in disjoint and/or individual signaldimension. Disjoint and individual signal dimensions are defined inspatial dimension.

Still another aspect includes a method of finding the common spatialdimension of plurality of transmitters and a receiver. The commonspatial dimension may be denoted by precoding matrices at thetransmitting point and receiver filters at the receiving nodes. Thetransmission from plurality of transmitters may be aligned in the commonsignal space. The transmission from plurality of transmitters may bereceived in different dimensions in disjoint signal space.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of theprinciples of the present invention and that those skilled in the artmay implement various modifications without departing from the scope andspirit of the invention. Those skilled in the art could implementvarious other feature combinations without departing from the scope andspirit of the invention.

What is claimed is:
 1. A method implemented in an access point (AP)having N antennas used in a wireless communications system including twofirst client devices each of which has M antennas and two second clientdevices each of which has N antennas, where M and N are even, the methodcomprising: performing interference alignment (IA) in common vectorspaces; and delivering M+N streams.
 2. The method as in claim 1, whereinthe two first client devices comprise a first uplink (UL) client deviceand a second UL client device and the two second client devices comprisea first downlink (DL) client device and a second DL client device, whereM and N satisfy M≦N, wherein the delivering comprises: receiving N/2streams from each of the first and second UL client devices; andtransmitting M/2 streams to each of the first and second DL clientdevices.
 3. The method as in claim 2, letting matrix A=[h₁, . . . ,h_(M), g₁, . . . g_(N-M)] where H₁₂=[h₁, . . . , h_(M)] is a channelfrom the second UL client device to the first DL client device andH₁₁=[g₁, . . . , g_(M)] is a channel from the first UL client device tothe first DL client device; finding vectors w_(k) that are in anintersection of images of transmit vector spaces at the first DL clientdevice according to the following equation:${w_{k} = {{\sum\limits_{i = 1}^{M}\; {\alpha_{1}^{k}h_{i}}} = {g_{N - M + k} - {\sum\limits_{i = 1}^{N - M}\; {\beta_{1}^{k}g_{i}}}}}};$generating full rank matrix C=[w₁, . . . , w_(2M−N)]; and determiningcommon vector spaces C₁ and C₂ as an inverse image of full rank matrix Cin vector spaces of the first uplink (UL) client device and the secondUL client device, respectively.
 4. In a wireless communications systemincluding a first uplink (UL) client device and a second UL clientdevice each of which has M antennas, a first downlink (DL) client deviceand a second DL client device each of which has N antennas, and anaccess point (AP) having N antennas, where M and N are even and M and Nsatisfy M≦N, a method implemented in the first DL client device, themethod comprising: receiving M/2 streams from the AP, whereininterference alignment (IA) is performed in common vector spaces, andwherein M+N streams are delivered.
 5. The method as in claim 4, whereinthe AP receives N/2 streams from each of the first and second UL clientdevices and transmits M/2 streams to each of the first and second DLclient devices.
 6. The method as in claim 5, wherein the AP lets matrixA=[h₁, . . . , h_(M), g₁, . . . , g_(N-M)] where H₁₂=[h₁, . . . , h_(M)]is a channel from the second UL client device to the first DL clientdevice and H₁₁=[g₁, . . . , g_(M)] is a channel from the first UL clientdevice to the first DL client device, finds vectors w_(k) that are in anintersection of images of transmit vector spaces at the first DL clientdevice according to the following equation:${w_{k} = {{\sum\limits_{i = 1}^{M}\; {\alpha_{1}^{k}h_{i}}} = {g_{N - M + k} - {\sum\limits_{i = 1}^{N - M}\; {\beta_{1}^{k}g_{i}}}}}},$generates full rank matrix C=[w₁, . . . , w_(2M−N)], and determinescommon vector spaces C₁ and C₂ as an inverse image of full rank matrix Cin vector spaces of the first uplink (UL) client device and the secondUL client device, respectively.
 7. In a wireless communications systemincluding a first uplink (UL) client device and a second UL clientdevice each of which has M antennas, a first downlink (DL) client deviceand a second DL client device each of which has N antennas, and anaccess point (AP) having N antennas, where M and N are even and M and Nsatisfy M≦N, a method implemented in the first UL client device, themethod comprising: transmitting N/2 streams to the AP, whereininterference alignment (IA) is performed in common vector spaces, andwherein M+N streams are delivered.
 8. The method as in claim 7, whereinthe AP receives N/2 streams from each of the first and second UL clientdevices and transmits M/2 streams to each of the first and second DLclient devices.
 9. The method as in claim 8, wherein the AP lets matrixA=[h₁, . . . , h_(M), g₁, . . . , g_(N-M)] where H₁₂=[h₁, . . . , h_(M)]is a channel from the second UL client device to the first DL clientdevice and H₁₁=[g₁, . . . , g_(M)] is a channel from the first UL clientdevice to the first DL client device, finds vectors w_(k) that are in anintersection of images of transmit vector spaces at the first DL clientdevice according to the following equation:${w_{k} = {{\sum\limits_{i = 1}^{M}\; {\alpha_{1}^{k}h_{i}}} = {g_{N - M + k} - {\sum\limits_{i = 1}^{N - M}\; {\beta_{1}^{k}g_{i}}}}}},$generates full rank matrix C=[w₁, . . . , w_(2M−N)], and determinescommon vector spaces C₁ and C₂ as an inverse image of full rank matrix Cin vector spaces of the first uplink (UL) client device and the secondUL client device, respectively.
 10. A method implemented in a wirelesscommunications system including two first client devices each of whichhas M antennas, two second client devices each of which has N antennas,and an access point (AP) having N antennas, where M and N are even, themethod comprising: performing interference alignment (IA) in commonvector spaces; and delivering M+N streams.
 11. The method as in claim10, wherein the two first client devices comprise a first uplink (UL)client device and a second UL client device and the two second clientdevices comprise a first downlink (DL) client device and a second DLclient device, where M and N satisfy M≦N, wherein the deliveringcomprises: transmitting N/2 streams from each of the first and second ULclient devices to the AP; and transmitting M/2 streams from the AP toeach of the first and second DL client devices.
 12. The method as inclaim 11, letting matrix A=[h₁, . . . , h_(M), g₁, . . . g_(N-M)] whereH₁₂=[h₁, . . . , h_(M)] is a channel from the second UL client device tothe first DL client device and H₁₁=[g₁, . . . , g_(M)] is a channel fromthe first UL client device to the first DL client device; findingvectors w_(k) that are in an intersection of images of transmit vectorspaces at the first DL client device according to the followingequation:${w_{k} = {{\sum\limits_{i = 1}^{M}\; {\alpha_{1}^{k}h_{i}}} = {g_{N - M + k} - {\sum\limits_{i = 1}^{N - M}\; {\beta_{1}^{k}g_{i}}}}}};$generating full rank matrix C=[w₁, . . . , w_(2M−N)]; and determiningcommon vector spaces C₁ and C₂ as an inverse image of full rank matrix Cin vector spaces of the first uplink (UL) client device and the secondUL client device, respectively.